Kids miss their parents, especially bad parents because they DESPERATELY want that parent to care. They WANT their parent to show them that they love them. But they also just love their parents and miss them. My guess is that the kids also miss their dad while with mom, and they likely feel more secure with their dad so they don't miss him as much because when they're together, they're connected. 

Regarding grandma, don't feel hurt that she'd rather have a relationship with someone who is dysfunctional and hurts her grandkids, and that she'd rather her grandkids have a dysfunctional relationship with someone who is in no position to be a wife or mother. The issue is with GRANDMA, not you. Your DH should call out grandma and cut her off if she's going to be disrespectful toward you. If he won't do that, tell him that he needs to not keep his phone on speaker because it's rude to be involved in a conversation that grandma doesn't want you involved in.

Finally, full custody seems like a good idea. It would be good for your DH to consult an attorney about what the chances would be of getting custody and what documentation he needs for court. And if your DH didn't contact law enforcement about her stealing his identity, he should talk to the attorney about that, too.

So I went back and read some of your past blogs. Although it is true that people are contradictory and can feel different ways, you've repeatedly posted about just how awful these twins behave. Not that it's their fault entirely! It sounds like they've received really poor parenting, both from their mom and from your partner. He has literally locked himself in your bedroom and said he can't stand his own kids, leaving you to do the care tasks. I understand that it would feel simpler if BM dropped dead and you raised the kids, but your partner is a terrible parent. He would end up dumping all three of his kids with other women on you, leaving you to play rescue were in martyr while his kids complained they missed their parents.
 

And also oh my God the BM is next-door to you. This is a God awful situation with no boundaries all around.

And to top all that off, it sounds like not only do you have a crappy partner with crappy children, but his family is crappy and treats you terribly. I don't know why woman number two is the person grandma thinks he should be with rather than the woman who bought his first child, or you, but these things don't change. Someone her age isn't likely going to say oh my goodness I have seen the error of my ways look at this wonderful caring woman you are with now. Between grandma and your partners terrible behavior and three kids from two different mothers, you were in for a lifetime of being treated terribly and receiving no appreciation, in fact it sounds like your partner already expects you and feels that you were obligated to care for his children as if they were your own.

I don't know how this can be the love of your life if he is this terrible of a parent and this terrible to you. I couldn't respect somebody who hid from their own toddlers, or who couldn't stand up for me with his family or ex. I know this wasn't what your post was asking about, but please make sure you were taking your birth control, and really consider whether or not you want to legally bind yourself to this person for the rest of your life. Good luck and Godspeed, I think you're gonna need it.

Good Luck

When you send pics to BM, cc GMa.  End of manipulation by BM towards GMa. It also tightens the boundaries around GMa and gives you fodder for ending her manipulative crap.

Make sure the email or text is clearly labeled with the date and "Skids, Dad, and Mm1985 at XYZ LMNOP".  If BM scalps your pics and tries to sell them to GMa as her activities with the Skids, give GMa clarity by telling her "Oh, their dad and I took those pictures when we were doing LMNOP with the kids on XYZ date.  You were on the email/text GMa."

Lather, rinse, repeat.

Keep it simple.

DH will get full custody if BM gives it to him, or she does something so egregious that CPS has to act.  Staying home with your kids and watching TV is not abuse or a reason to change custody. Lots of kids watch TV, eat cold pizza, have had someone to tell them to "shut up" and have survived.  Yes things will be different in both houses, welcome to blended families and coparenting.    

Do you have proof she shoots up?  Has this been reported to CPS? Has your DH filed for an emergency Change of Custody due to this behavior?  If yes, then your DH has done his part, if not then he needs to stop whining and do something about it if he truly believes his kids are neglected and in the care of a drug addict.  Most SM's immediately regret it when their partner gets full custody. Dads are happy because they no longer pay CS, then pawn the kid(s) off on the nearest female in their life. 

About grandma, who cares! Lots of people send grandparents pics of the kids. My exMIL was very vocal about wanting my then hubby to get back with his high school girlfriend.  In hindsight I wish he had LOL.  

Sounds like some disengaging is in order. Best of luck with your husbands situation.