This "worker" is giving you empty threats. I knew she couldn't be a real social worker. Don't depend on her to have the faintest idea what she's talking about. She has a high school diploma and, maybe, a tiny bit of training. Isn't she supposed to be helping you with housekeeping? No one's taking your kids anywhere. So focus your worrying on real problems.

Don't "bring up moving out" with your dad again. He's never going to give you his blessing on that. Just pursue doing it. When you get a place lined up, simply notify him shortly before leaving. He'll have to learn to solve his problems without you. He will.

What would happen to your kids, if you committed suicide? Keep that in mind.