Covering your spouse's health insurance after being separation

Hello everyone,
I'm new to this forum and I'm hopeful I can get some advise regarding my above titled subject.
I came to Germany with my German husband and child many years ago. Since a few years we've been separated and I live with our child. I unfortunately, have been on Hertz lV since a couple of years. Recently my ex (I'll call him that though we're not divorced yet), lost his job and is currently in the hospital and might need a longer term clinic. He lives with his gf in another part of Germany. His gf was informed by his insurance (same one as mine) that I can include him in my family insurance with no extra charge till she finalises his unemployment paperwork as he's entitled by law to this. Otherwise, she'll cover his insurance by paying for it herself. I called the insurance myself (talked to a different person) and was told the same including that if I don't he could go to court to obtain this.
I also asked the Socialamt who warned me not to include him as it'll cause problems for me with them and could reach to police involvement. The insurance confirmed they do not send any paperwork regarding him to my partner at Socialamt but eventually I believe they must as his name will be a new addition to my family insurance which is covered by my Socialamt. I don't mind helping him if it won't jeopardize our only current income. Do I need a lawyer?
Anyone know anything about such matters or has been through anything similar? I'd be grateful for any constructive comments or advise. Feel free to ask more questions if I've been unclear. Thank you for reading.