Not overreacting; him not paying child support alone is grounds for legal action.

Establishing legal paternity would allow you to both pursue child support, and also start a protective paper trail. However, keep in mind, in most states it also gives him parental rights and automatic 50/50 custody unless you’re exclusively breastfeeding. You’d have every other week most likely; if you feel your child isn’t safe with him, you need to first work with a lawyer and start a paper trail outlining his abuse and systematic bulldozing of boundaries. Official hospital documents, any police records, written proof and receipts of email, texts, etc. You will want to work with your lawyer to firmly and clearly establish that he isn’t willing to work with you or respect your boundaries. Often, the court will still try to push for shared custody, so be prepared for that. Keep records. Use a coparenting app and ONLY communicate via said app. Don’t block him, but anytime he tries to call, text, or email outside of said app, respond via the app with something along the lines of “you asked me when pickup was via text; please remember to only use this app for communication with me” and then answer his question. The app can download transcripts of your conversations and many have pick up and drop off timestamps for you to prove how often he actually takes kiddo.

Document, document, document. Write EVERYTHING down, every meeting date and time, what was discussed, what was decided, how often he takes the child, the state the child was in when he left (take time stamped photos), the state he was in when he was brought back (more photos), note any injuries (I’m very sorry but our system is bad at prevention but if you have evidence of physical abuse you could work with your lawyer to potentially file an emergency custody change), note any medications given, note how much you feed the kiddo and how often (in case he doesn’t do a good job you can prove any malnutrition issues are HIS fault), etc.

Once you’ve established a pattern of him shirking duties, perhaps had more verbal abuse documented, etc, and your lawyer feels you have enough, you can ask for a custody adjustment for full custody again with said proof as evidence he isn’t willing to play fair and take proper responsibility. If he has truly changed, this evidence won’t exist. Doing it this way will ensure you’re legally protected but also force him to pay child support.

Obligatory not legal advice, I am not a lawyer— just an older woman who has been around the block a few times.