First.... take a very good and hard look at your relationship and at this guy.  Is he really the most perfect person you thought you would be with.. do you feel he is a partner to you for life?  Because steplife is hard.. and it comes with drama and struggle.. and it sounds like you may be kind of young.. and perhaps you might be better off seeking out a partner without the baggage.  That IS an option.

Second... women have a horrible habit of "auditioning for the wife role".. don't fall into the trap of showing off all your homemaking skills.. acting like the doting caretaker of his kids.. if you truly don't want that to be your life.  But.. also consider that with kids that age.. there can and will be times you will have to partner in caregiving with him.. do some babysitting.. help him with the kids in your home (if you move in together).

Third, The calling of mom and dad.. I think you and he need to have a discussion of what you want to be called.. even if you become stepmom.. you still may NOT want to be "mom".. and for many reasons including the fact that if you let them call you mom.. their "real" mom can get jealous and really ramp up drama.. don't fall for that trap.  My DH's kids called me by my first name.. period.

Fourth... the incident with the kids is worrisome for two reasons.. First.. I think you should have realized that gum wasn't a good candy to give the kids.. the mess.. the choking hazard.. it was not great judgement.. BUT.. your SO should have tried to be more kind when he helped you understand why it wasn't a good idea.. is that a window into your future life.. ?

And.. I get that you don't know much about kids.. I can feel you there.. When I had newly started dating my DH and his kids were 9 and 5.. we were at a Target and the 5 yo said she had to go to the bathroom.. I volunteered to take her.. thinking she was old enough to potty on her own.. but.. I take her in.. stand outside the stall holding it shut.. and she calls out.. "you have to wipe my butt".. so... I had no idea.. maybe 5 year olds DO need their butt wiped.. So.. I got a big ball of TP and did my best.  I went out with her and whispered to her dad.. "you could have told me she needed help wiping".. he looked at her and sternly said.. "YSD.. you know how to do that yourself".. she just giggled.. at her big joke she played.. I told her.. Oh.. don't worry.. this is a memory I intend to hold on to.. and repeat to all your future boyfriends..lol.  I mean.. we don't know everything if we haven't had kids I guess...haha.

PERIOD. DOT!

Also, BF Is the breeder. You are not. So, care and oversight of his breeding results are on him, not you.

If his young spawn have a meltdown in public, that is on him. Whether he is dealing with salespeople or not.  Let them melt down. Just step back and let them melt.  Keep an eye on them to make sure that they are not in jeopardy, but... do not intervene.

If this is how he is with you when you do not live together, consider how he/they will abuse you if you move in with him/them.

Move on. Find a person of character who puts you and the relationship above all else. Including any failed family breeding products.  Even in Unicorn SParent/blended relationships SParenting is challenging.

Not your spawn, not your problem.

Time for an if. A big IF!  If your BF is clear that it is his job to parent to YOUR expectations. He may be salvageable. Though that is not likely.  Many SPs step back, abdicate a huge portion of control of their own lives to a prior breeding new mate.  That cannot happen. Ever. IMHO.  Equity life partners are also equity parents to any spawn in their home/lives. The breeder in the relationship owes their mate peaceful calm and must hold their failed family spawn to that commitment.  

As it turned out in our marriage, SS-31 is an only child for us.  We met when he was 15mos old and married the week before he turned 2yo.  Neither me nor DW would have tolerated anything less than an equity life partnership including equity parent status.   When we had the occassional disagreement on parenting and discipline I gave the message "If you don't like how I parent and discipline then you had better step up and deal with it before I have to. Or, have my back until we can discuss it in private."

Overall we partnered very well in raising SS-31 to viable adulthood. He is a good man. Our son (He asked me to adopt him when he was 22. We made that happen though I have always been his dad.) man of character and honor, successful in his career and life, and a man of standing in his community.

If you do not set the standards of behavior and standards of performance for your SKids and your SO, you are in for hell.

As for being called Mom.  I take the position that I do not allow children to call me by my given name. If they are not my niece/nephew, they call me Mr. Last name and Sir.  Period. Not their choice. Not the choice of their parents. I alone set what children refer to me as.  As for SS.  I was the first person he ever called Dad(dy).  He made that choice before he was 2yo.  We did have  a couple of incidents where the SpermClan took exception to it, but... they got no say.  You decide what your BF's kids call you. You and only you.

Take care of you.

That you are not living with him.  You go home at night and decompress.  If you move in and he has the kids 1/2.the time. Your role in the family becomes different,  he going to leave the kids with you. He will have the kids , something comes up that he going to have to handle. You are babysitting...  

BM isn't going to be happy. Having another woman,, any woman. Takeing care of her kids.  BM rules.  Bed time, homework etc. will be Different then yours.  YOU..  will not want BM controlling your home. BM bed time is 11 pm. Yours is 9 pm.  Of course kids will complain to BM.  You want time with SO. Here's a Fight with no way, for anyone to win.  Your house your rules BM is mad kids are mad. 

I've been an SM for 28 years and not a day goes by that I don't regret marrying a divorced dad. Not a day goes by that I don't wonder about how my life could have been had I held out and married a man who didn't already have brats. My DH and I have recently been through over two years of intensive therapy for both of us individually and as a couple and things are way better, but still not ideal. I really wish I held out for a man with no kids. I wouldn't wish it on my worst enemy. Speaking of worst enemies, my worst enemy for many many years was my SD34. And don't think it can't happen to you because you're starting out with your SKs being so young. 

I was 31 when I met DH and I settled. Yep, I said it. I settled. I was co-dependent back then and was single for a long time and thought that if I didn't settle, I'll never get married. God, I wish I wasn't so fucked up like that because I would have not even considered a date with a divorced dad.

The fact that your potential SDs are having meltdowns in stores and calmed when they got candy tells me that they have been through that before. I wonder if your SO went and talked to the salesperson for a while because he wanted to avoid his kids' meltdowns. I don't know. You might want to consider it. Or maybe he put you to the test. I wouldn't put anything past a bio parent after what I've been through.

Please go back and read Rags' comment. I agree that the bio parent owes their new partner peaceful calm by holding their ferals to standards of behaviours in the home and towards you. This forum is full of SMs to Disneyland dads who not only do not provide their new mates with a sanctuary of a home, but they put the onus on the SM and expect her to eat shit and suck up to brats, sometimes totally abusive ones. 

Step-parenting is extremely hard even in unicorn cases where there isn't Mini-Wife Syndrome, Disneyland Dad Syndrome, Parental Alienation by the BM or high conflict Golden Uterus BMs. Then there are cases of divorced dads who are scared shitless of their exes and leave their balls in the BMs' purses and set you aside like yesterday's leftovers. There are divorced dads who haven't "done the work," and aren't over their exes or demise of their relationships and are subsequently not able to be all-in with you.

I'm concerned about your SO's reaction to you. He didn't seem to have any compassion towards you for not knowing what to do to circumvent a tantrum with both kids in public and he didn't seem to put himself into your shoes at all. 

Do some searches on here for the syndromes I listed above. Do reading on here. I say this because hopefully it'll give you some food for thought and better yet, you'll save yourself from a horrible fate and get the hell out. Go live your life. Go travel with girlfriends or on your own, take courses, take up hobbies and go find a man with no kids. You feeling alone and unsupported at the store is only the beginning of a long pattern of feeling that way. Please heed the red flags. Maybe make some other blogs or post comments of some other incidents that you're questioning. I'm so glad you're here because it means you're questioning what happened at the store and how your SO reacted to you causing you to feel alone and unsupported.