Time to step back. Court gets ugly usually. If he has custody all this time and kids are started school then it should stay the same but she will have some sort of visitation.
How far away is she now? Is she in the same school district?
Joint
legal custody really does not mean too much so do not get hung up on that. It just means they both have say in any school issues or medical issues. It is the visitation part that you have to hash out.
Start the low contact with her, especially during court. Use email to tell her children issues but only big ones, school activities, visitation issues. If she writes back, answer with one sentence or ignore her if she is just ranting. Everything should be signed by you BF only.
Legally you have no say in any of this and never will even if you marry. Step parents have no legal rights. Just go on your day and deal with the fall out of her time with them. Teach the kids coping skills as they get older. Do not talk about court with kids. Just say this is for the adults to talk.
For court, get binder of proof that he has kids, dr appointments, dental appointments,
school records showing his address, first
report card. Mom will get some sort of time unless you can you prove neglect. Usually if she is closer than 60 miles she will get every other weekend, and maybe a night during the week for dinner visit.