Need some advice...

Ok so i dont want to be bashed or have rude comments please. So im lesbian ive been with my partner for 7 years and we are married, well we devided after a long time of debate to get pregnant, we went with a really good friend of ours and had him be the doner because its really expensive for us to conceive <a href="https://glowing.com/glow-fertility-program">ivf</a> or otherwise or adopt. Anyways, so my wife was hurt in an auto accident and has not worked since well im going to be having our baby in may and finances took un unexpected turn.... we have talked about having the father on the birth certificate because I can no longer provide the baby with insurance myself untill i get a better job. He has good insurance and he said he would help us and put the baby on his insurance. Well idk how comfortable with this i am. I understand that the baby needs insurance thats the only reason i would do this. But i am afraid that if for some reason things went south he could file for custody and take our child away. Or try to. We live in arizona, and from what i have found if i ask for state help they go after the father no matter what but idk if that is true. If he isnt on the birth certificate they can find a way im sure to find who he is. I dont want child support at all. Im really in a mess and i dont know what i should do..... would a lawyer help ? What should i do i need suggestions all i want is whats best for my baby and we thought we had it planned just didnt expect to loose an entire income and be just living off of one which we are bary holding it together even rented the rooms in our house to make ends meet since. Advice please anything....