So heartbroken about my fathers child

So my ex refuses to sign a voluntary acknowledgment of paternity form. Now he's questioning if he's even the father so I said fine, I'll do a non invasive paternity test but in both California and Nevada (where we have lived) the alleged father has to pay for that by law and it's not cheap. He called me crazy. I even told him all the information for him to terminate all parental rights of this child so the parent-child relationship is completely extinguished, he will have no responsibility of the child and no longer have any obligation to provide care or financial support. I sent him that information because with his absence and attitude it just seems like that's what he wants. Basically I'm giving him an out. He's lazy, won't respond about it and wouldn't even answer my lawyers phone call this morning. He blocked me on everything too. Been super immature. Now I have to have my lawyer draft a paternity case. That way when it's submitted to court, a document will be served to the suspected father ordering him. If he does not comply, legal action will be taken and possible jail time. I've been so patient and kind. I just want what's right for my child. I'm sending the documents to his work. I'm going to subpoena his boss because he is the custodian of record. If i send it to his apartment he can deny it. With his boss being involved my babies father can't walk away and say no I have not been served. He's been awful this whole pregnancy. I've been hospitalized due to my excessive throwing up and he didn't come visit, I got no calls or texts asking if the baby or I were doing okay. At this point I don't even care about child support, I just want this over with and for him to be out of our lives and sign his rights away. I don't like the people he surrounds himself with. That's what I am most concerned about. I just want my child to have as normal of a life as possible and not question if they are wanted or not. He thinks I'm chicken shit and won't go through with anything. He can't just come into our child's life whenever its convenient for him. He's so back and forth and questions everything; but when it comes down to it he does nothing about it. I've given him countless chances to man up and be an adult. I'm disappointed in his character and motive. To even question my morals like that is unbelievable. Just because he wasn't loyal doesn't mean I wasn't. My heart is so tired and it's not healthy for me or the baby to be so stressed about uncertainty. I'm a 22 year old single mother, I want this all figured out by the time the baby is born. You would think for him being 28, divorced and already having a child he would be more mature. Any advice ladies? I can't afford too much but I will go to any length for this child and what's right. I just want to know if you all think I'm handling this well. I feel like I'm going crazy.