If you decide to stay together no matter what you do, do NOT move in with him. His jealous children will destroy your relationship faster than the speed of light because they want daddy to themselves. Daddy is completely ignorant (or naive) to that fact. If he is good to you stay with him on the conditions that you will not marry him nor move in until his kids are grown and out of the house. If he cannot agree to that I suggest staying single and dating.

If you decide to stay together no matter what you do, do NOT move in with him. His jealous children will destroy your relationship faster than the speed of light because they want daddy to themselves. Daddy is completely ignorant (or naive) to that fact. If he is good to you stay with him on the conditions that you will not marry him nor move in until his kids are grown and out of the house. If he cannot agree to that I suggest staying single and dating.

 My SO blames me for not being sympathetic enough. 

What is there to be sympathetic about? You're the one who is subjected to unruly, ill mannered kids and he wants YOU to be more sympathetic? How about he starts parenting his kids and show them how to be respectful and have manners. How about SO having a talk with his son about comparing you to his BM and shutting that sh!t down. You're not being petty because these are red flags......flags that have been ignored by many on this board and are here now posting about it. You can save yourself the drama and not marry him. Unless he makes changes on how he parents I wouldn't entertain the idea of marrying him. You'd be in for a lifetime of stress and chaos with a man that can't/won't parent his disrespectful kids.

ETA: He has already dumped you once, take that and move on!!

Why is it petty to expect his kids to have respect for an adult in their life?

This is where to many SM's and SM's to be fall into the trap of thinking they must somehow prove themselves to their potential mate. Make him prove to you why he and his kids are worth your time and energy! Flip the script, make him work for you, make him have his kids show you respect to see why you would want a future with him and them in it.

He has dumped you before and you don't like his kids...
Why are you still in this relationship?

I feel for you so sorry you're going through this. I'm in the same boat as well and it isn't pleasant! I wish you the best!

Why do you love him dearly exactly? He’s a crappy parent and plays games with you, breaking up with you and then trying to get back together.  A man should only get one chance to dump you. 

Find a better guy. They are out there. 

Going by your earlier post in which you said your boyfriend dumped you, and this one, it appears the whole family are manipulative and spiteful, and your boyfriend supports this against you. Why then do you "love him dearly"? what exactly is it about him that you love, when he doesn't hesitate to throw you under the bus for the sake of his poorly behaved children? 

Zero tolerance works.  Jerk a knot in the tails of the little shits for their spying crap, their whining and their crying.  If you are at an event that you have paid for you get in the SD's face, poke her in her chest and tell her she is not going anywhere and will participate and keep her mouth shut or she will find out what being miserable feels like. 

DH needs this message too. His kids do not spy in your home. If they come to him tattling on you, he needs to immediately put them over his knee and warm up some butt.  He also needs to let them know that they do not spy for BM either and if they are.. it will be even worse for them.

I had to apply a lesson to both my SIL (DW's youngest sib) and my MIL though not on spying and there was no butt wuppins involved.  The People's Republic of SpermLand changed the graduation requirements for HS which allowed my SIL to graduate a year early with my IL's permission.  We begged then to not let that happen because SIL needed that year to mature.  Nope, they signed. To attempt to save her from that shitty decision I suggested to DW that we offer for SIL to join our home, we would take guardianship, and pay for her college.

Even my ILs recognized this as a very generous offer and great opportunity for SIL and put their collective foot up SIL's butt to take our offer.

A year later she turned 18 and decided to run back to SpermLand to pump out illegitimate spawn with her BF.  She did fairly well her Freshman year of college because my bride and I would not let her skip class or turn in shit work.  She was miserable because we forced her to rewrite papers over, and over, and over again, we expected her to deliver on her commitment to keep the house clean, do the lawn, and be there every afternoon when SS got home from school.  

She called MIL and begged her to come get her and bring her home.  We had purchased a vehicle for her to drive when she lived with us to get to class and schlep SS and his friends around with.   I signed it over to her when she insisted on moving home.   I was on a rotational assignment at that time and flew home every Friday evening then out again every Sunday evening.  I had outlined service that she needed to get done on the vehicle before driving it the 2500+ miles from our home to SpermLand.  Which of course she didn't do.  I spent that weekend working on the vehicle, getting the cooling system serviced, and had to put a new set of tires on it.   When I pulled into the driveway Sunday evening with a fully serviced, safe, and newly shod vehicle after spending my entire weekend addressing bullshit she was supposed to have had done rather than spending time with my wife and Skid I was about to blow a gasket.  DW came out and I walked her through everything I personally did and what I had done.  SIL and MIL were inside putting a puzzle together. Which was the last straw. I told DW that she had best get her idiot sister out to go through everything with me or I was going to drag her idiot ass out by the short and curlies.  My wife had never seen me that irritated and knew she had better be the one to go get her sister or it would likely not be pretty.

She came out with SIL and I went through everything with her.  She just stood there with her arms crossed and a sour look on her face.  When I finished by reviewing the tires with her and having her check the tire pressure she huffed and said ... they're tires, so what?  Daddy says that new tires are a waste of money and it is cheaper to buy used tires. They are just as good.   My MIL was standing in the door also with her arms crossed because I had interrupted her and SIL's puzzle fest.

After SIL's snarky tire comment I climbed her ass and let her know that driving across the country on worn out old tires was just F'n stupid.  MIL says from the door "If this is a problem we will just fly home!"  I turned purple and said "Oh hell no you won't. First you don't have the money for plane tickets and you and your idiot daughter are going to drive this Jeep every inch between here and your home if I have to follow you and kick you two in the ass every inch of the way!"  My wife knew how pissed off I was and just put her hand on my shoulder to calm me down.

That evening it got worse.  SIL was supposed to have gone to the County Tax office to transfer the title of the vehicle to her name. I was not going to have those two dipshits driving a vehicle that was still in my name across country.  I had given her the money to do it a the week before.  She didn't do it.  When we sat down that evening to give her the owners manuals, tire warranty, etc, etc, etc... I asked where the title was.  I got the big eyeball empty brain look followed by the eye roll and crossed arms huff.  So.. I rebooked my flight which was scheduled to leave in 3 hours to Monday evening.  The next AM I dragged (not litterally) SIL and MIL out of bed and had us standing at the tax office when it opened Monday AM.  Once SIL had the title put in her name I schlepped them back to the house, herded them out the door with their shit and ended that shitty year.

I ended up reschedling my flight a second time to Tuesday evening because my bride and I wanted a couple of days of calm for just the three of us.

Love is earned with respectful loving behavior.  If your DH's kids are not earning your love, then let the kids and their father know, outline the issues, and state clearly what will no longer be tolerated.  DH needs clarity on this as much if not more than the Skids.

The vehicle incident with my SIL and MIL was the start of behavioral change that made them tolerable.   My SIL has proven herself to be a dirtbag of monumental proportions but my MIL has actually evolved to a point where I have some respect for her.