The most important thing to remember in this situation is that your boyfriend’s kids are grieving. Their mom abandoned them. They lost her and the home they’ve known. From their point of view, they can’t trust you or their dad either. They think that since their own mother could leave them, so could you. These kids aren’t bad. They are in enormous emotional pain. Being kids, they don’t have a way to understand what has happened or to talk about it clearly. They act out instead.
Family vacations and movies, though wonderful family outings, are not going to balance out their feelings of anger and sadness. Then need support in dealing with their feelings. You and their father need support in learning how to support the kids. This isn’t easy stuff. But it is essential. You want to stabilize things before they get into adolescence, when kids normally push away from parental influence. You want to lay in trust and love and understanding now that you will be able to draw on later.
Your instinct that it would be a good idea to see a therapist was on target. But the whole family needs to go, including your 3-year-old, not just the daughter. You all need to have a place to talk about how difficult the situation is for all of you and to figure out how to live together and, hopefully, how to love and trust each other. A trained family therapist can help you with that project.
Please follow through. If you could have handled this on your own, you and your boyfriend would have fixed it already. I can tell you care about these kids and have compassion for them. Now you need some new skills.
I wish you well.