Something tells me that this name thing isn't the only boundary of yours that's been stomped. Call yourself what you want but let the kids call you something that won't incur the wrath of the harpy. They probably get in trouble at their mom's if they call you stepmom. 

She sounds psycho. Block her. 

While society would want me to be called SM, I am not. And after 12 years of BS treatment by his adult kids (soldiers in the BMs war), who influenced th two younger ones, I refuse to be called a SM. I married DH, not his kids. They have two capable parents...well, they did. BM died a few years ago but after what they've done to me, no way would I ever step into that role. 

In the case of your BM, please read some posts on this page and set yourself some healthy boundaries. As someone said, BLOCK that BM. You do not need to be in contact with her, on social media with her, etc. NOTHING. It is your DHs job to communicate with his ex. I encourage you again to search this site for disengagement and techniques on how to deal with PAS and High Conflict BMs. Get yourself "educated" on the High Conflict StepHell you are in. 

You shouldn't have to manage boundries with her, she's not your ex. That is 100% on your husband - she is HIS mistake, not yours. 

IMHO he should be telling her to butt tf out of what happens at his house, she can manage er own.

They can call you Dad's wife.. that is true correct?

You can refer to THEM as you wish.. you are both dad's wife.. and a stepmother to two children.

As far as addressing you... they can call you by your name if that works for you.. my SD's called me by my name at MY request... I did not want them to call me any version of "mom".. but they did refer to me as both Dad's wife or my Stepmom when speaking to others about me.. both were correct.

Given the mother's strong stance on this.. I would not put the kids in a position of having to disobey her command.. but simply just have them tell people you are their dad's wife... if anyone says.. that makes you their stepmom.. they can say.. yeah.. I guess technically it does. 

What boundaries are in place in your home as far as being respectful to you.. those are more hills to die on vs some "title".  

I would also be pretty low key about posting things as if these were "your girls".. and "bonus mom" "blended family" hoo ha on social media too.. sounds like the EX is a big enoug PITA.. no need to get in a territory pee match with her.. because the people it will really end up hurting are the kids.

The insanity of BM. Always finding conflict. Just another way to stick it to the SM. Shame BM has no confidence that she isnt being replaced as the mom.

Frankly I am old school and skids calling by first name puts the skids on the same level as you. Thats just IMHO

Simple really, the SD's AND BM should call you Queen, and courtsey every dang time you allow them in your presence. LOL

Seriously, I wouldnt fight this, it just aint worth it. I totally get the WTF does this matter to BM though. If you are comfortable with them calling you Cynthpop then go with it. 

Or "dad's amazing wife"  Works for me. 

Spawn just called me by my name, it was honestly what was most comfortable for both of us.  I could give a rats a$$ how Meth Mouth felt about stuff, she was a junkie who didn’t deserve her kids, but I also wasn’t bio mom so I didn’t try to force a kid to call me mommy when I wasn’t.

For you.  Unfortunately she is doing it through the SK.  Those kids have two parents,  you are not one of them.  No one told you to get involved in SK life's.  To take care of them, to bond with them.   Unfortunately you put yourself out there. In a prosistion  To get hurt. And BM did it.     Where is your SO in all of this ??

I might point out for your own consideration that you have been in these kid's lives for 6 years.. at this point.. they likely have formed the relationship dynamic with you already.. if you have a good relationship with the kids... it's not really anything that should impact you and them.

Now.. if you think that maybe this is coming about because you post a lot about her kids on social media.. use terms like "my kids".. post as if they are your children etc.. and these posts are public where BM has ready access?  you  may have given her the impression that you are somehow trying to take over her place as mother.. and while I get that you may provide a lot of care for these kids.. and even if  you think you are a "better" mother than BM.. the fact remains that she gave birth to these kids.. not you.. and maybe in the interest of not putting the kids in a bind.. not trying to broadcast your relationship with them could be helpful in not making their mother feel threatened. 

I am not saying you ARE doing that.. but IF you are.. I can see how she could be reacting like this.

It's just really sensitive to some women whose identity is very wrapped up in their kids and being a mother.. you appearing to step into that role is difficult for her to accept.

And.. if there have been a lot of conflicts.. this could also be a way she is trying to bend the narrative. 

To be clear the kids can easily call you dad's wife.. say.. "dad's wife is great'  "we like dad's wife" to people.. the word stepmother can be avoided if that is too triggering for their mom.. just make it easier on them and not make a big deal out of it.. and it won't be a big deal. 

I know.. it's stupid and petty of her.. but you can't stop her from being herself.

BM tried to tell the skids this when DH and I got together, and then repeated it to them after we got married 2 years later 'Floral is not your SM'. They figured it out for themselves and eventually agreed with DH when DH said 'She is your SM and one day BM will have to accept it'. Now they refer to me as their SM but call me by my first name. They only refer to me as 'Mummy' when talking to DD2 as in 'Go show Mummy' sort of thing. 

I advise you to stay out of it like I did and I told them they can call me and refer to me whatever they like except for Mummy because I found it awkward and wrong. SD3 always tried to call me that at the time and DH had to be really firm with her to stop.

BM of course got a BF and immediately makes the skids refer to him as SD and call him 'Dad' which the skids could see DH got annoyed at and definitely do not call him that.. and refer to her BF children as step brothers and sisters. They call his parents 'Gran and Gramps' and his sisters 'Auntys' and it makes DH and I skin crawl with cringe. BMs BF also has a small 2 year old and SD says BM allows him to call her 'Mummy'. Of course she does! Double standards ate strong is this HCBM. 

Anyway your SO needs to take control of this and tell your skids what's what if that is what you want. I think DH even at one stage told BM to stop manipulating the skids to not see me as a SM. Just tell the skids let them call you want they want as no doubt they are conflicted by their evil mother here. 

She gets no way in anything in your home and family.  She  is kart if neither.

If your DH does no keep his X in line, out your foot up his ass too.

The same goes for your SD's.  No one else can stipulate how you identify and facts are not negotiable.  BM gets no say and her lack of confidence is not your problem.

You are their StepMother.  Plant your flag on that hill and defend it.