She broke up with him because she didn't want to spend time with him nor their children, she'd rather spend time with her friends.
So how comes your partner is okay with that and tries to pretend nothing happened? Kids aren't stupid, and staying with someone who doesn't care for them can seriously damage their mental health.
people have wanted to bring social service on her
So WHY is your bf desperately trying to make this work? Srsly, HE needs to step up and protect his kids. If people will call CPS on his ex, HE will also be affected by it. Furthermore, his kids might easily resent him in a few years for letting them suffer for so long.