Whew! You have a lot going on in your life. It is hard to be a step parent. It is hard to be a parent! Nobody born came with a book of instructions. BUT. I suggest you check out books at the library or at the book store on this very issue. Step parenting. The books are out there. I have seen them. Also, look up on the internet about step parenting.
One thing, the oldest boy has got to toll the line on bullying, violence, lying, cheating, stealing and abusing his little brother. If he demonstrates this behavior mostly after he returns from his mother's, then you know where much of this behavior is encouraged and you had better just keep him home. He has psychological problems that he doesn't know how to deal with except whatever way that works for him. It may be more helpful to get him some counseling so he can learn better coping methods and reduce his anxiety, fear, anger, possibly depression too, and distrust of other people, and abandonment.
The children are playing you like a fiddle with threats on living here and then there etc. Your husband needs to be the leader in your household. They are his biological children. You need to back off and let him do his job as a father. It sounds like he is struggling with stepping up to this plate. He needs to seek counseling regarding parenting skills or start reading books on the subject. The boys need to feel more security in their lives and to feel their Dad will protect them. He needs to establish boundaries within your home, within the kid's lives. They need protection from themselves and are too young to know how to have it in a healthy way. Your husband has got to be their leader. Not just present. But an active leader in the home.
The fact that the mother is moving to another state, farther away much less, making herself even less accessible to her children is a pretty loud statement. She doesn't want to be around her kids. She is making visitation even harder for them. She is pushing them away from her. It is obvious she is self-centered and not mother material. She can blame everything in her world on your husband while refusing to recognize that she is not dealing with her issues, or providing support financially as well as parentally. Your husband should make it clear to her that the children are not to be used as pawns in her war with him. She must speak directly to him. Not attack him in front of his children. They don't know what to believe, what to think, what to say. They love both parents and it is unfair of her to make demands they choose one side or the other.
Your husband can go back to family court and demand that she pay child support or be arrested as a dead beat parent. He has every right to do this and if he doesn't then he must look within himself for the answer why. It is not your place to fight his battles.
Should their mother actually move away, I recommend that your husband deny the children their wish to move with her. They need to live in a stable home, know what it is to live with love, being wanted, a stable home, having boundaries they have to live by, and the older one needs to learn that his behaviors are not tolerated in the home or elsewhere, especially to his brother. And his brother needs to know you will protect him, that he is safe. They both need to know that home is a soft place to fall at the end of the day.
Victims of abusive homes tend to gravitate toward their abuser trying to appease him/her, to gain love, attention, safety, by doing everything the abuser wants. They become entrapped because the abuser never changes, and they are always getting mixed signals. " I did what she wanted but she still hates me. I must try even harder." Nothing will actually change with the abuser. The child will eventually, already, start hating himself because he can't get the love and attention he so desparately needs.
Do you have him signed up in sports, soccer, swimming, tennis, track, etc. He has lots of energy that needs to be burned off in a healthy manner, as well as to build his self esteem. You must decide if your boys have too much time on their hands right now. And if they do, get them into activities now. Let them equate blowing off energy with fun.
Their Dad and you must attend all of their parent teach conferences, band or play performances, games they are in. They must know that they are this important to you.
Do you do family outings, like travel, camping out, scouts, biking together, picnics, the beach, fishing, playing volleyball with them, swimming, taking walks together, sharing stories about your lives that are entertaining for kids, doing artwork, building things etc. These things all count as I love you and we can have fun together as a family. Take your kids to movies that don't demonstrate violence. Don't let them sit in front of the TV because it is a good babysitter. Have specific shows and the rest of the time they must play outdoors. Burn off energy. make friends. Teach them games to play with friends. This aqll gives them healthy social skills.
I know this has been long winded. But I think you have got the picture. You must NOT be the policeman in your family. This is your husband's job. You can be a protecter and enforcer of his plan, but the kids know you are a step parent, not their real mother. You don't have to replace her. You only need to make sure the boys are safe, loved, happy, wanted, and that they must deal with their father if they break rules he has set down. Good luck.
Is Mark still married to his wife? Are you and Mark married or just living together? I am not clear on this.