Mother wants to say my child is hers!

So I'm 22 almost 23 in couple months. My SO and I live with our own parents until we can get our financial situation in good standing. Which is hopefully until Jan next year. I am currently 19w, due in March. When my parents first found out they told me how they'll help support me and how I don't have to get rid of the baby. Which is something I don't even want to think of doing (please don't have a debate on whether it's right or wrong here; to each their own). Some time later they told me how they would drop me and the baby off at a shelter since they do not approve of me staying in the house with a baby. And how my mother said she'll call cps on me to take away my baby since she thinks I won't feed the baby. I'm still pregnant and wouldn't dare think of hurting my unborn child. Then tells me how they want me to buy a pack n play to leave at their house so they can watch the baby, etc. This makes me so confused. Today my mother told me not to tell anyone on her side of the family because she wants to tell them it's her child she said she just to see who would believe her. I told my SO and he was livid and told me not to let her do that. Now my parents are telling both their families how my SO isn't around and doesn't want to take care of the baby. When in truth he puts me and the baby before anything. And I honestly had planned on been moved out last year but unforeseen financial difficulties kept happening, college and now being pregnant. My SO parents will charge us if I move in with him and we just can't afford that at the moment. But at the same breath if I am still being physically abused by my parents then I can move in immediately without them charging us for a little while but nothing has happened in months. (In the past my stepdad choked me because I didn't answer the phone. It was acting up& didn't even ring and tons of other stuff) 
*Yes I understand if you can't take care of a child then birth control but my daughter was an oopsie but nonetheless a beautiful blessing. So what I'm asking is what do you think I should do? And apologies for how long this is.  
*MORE INFO: You guys are assuming we are jobless, etc!!! I never said we don't have any jobs. He's working 2 and looking for a 3rd and selling all his belongings that he don't need. Such as games, etc. He's doing so much and still applying to higher paying places but nothing. and I have one as well working full time but I currently pay about $700 a month to my parents and then some just because. So no, mommy and daddy are not tired of me. If anything Every ~5-12months my stepdad will lose his job. So I am constantly paying for bills. They see I am in a situation and want to take advantage.
 Currently working with a social worker (WELFARE) for months. There was a mix up at my job with how much I get paid and still haven't heard back. You can't call them, they call you. If you try phone #1 (A number they gave you to call) it will say call a different number, when you call that number it will say call the first number. There is no customer service or operator!!!! Believe me I have tried and tried. 
If I go to his parents we won't have enough money for food. I stated we are in a 'financial situation'. We're currently trying to save all the money we can for the baby till his permanent government job starts in January. So a few months from now we will move out to our own apartment. I said I didn't want to start a debate on pro choice. why? because I'm asking for advice on my current situation not asking whether it is right or wrong. my parents are acting all gushy on all the things they're going to do for the baby. Like how I should leave her at their house so they can teach my teen sister how to take care of a baby. I want to just leave my family behind but that also means my grandmothers, sister, cousins and the rest of the family. They will out me and say a bunch of lies and make it so I can't even get in touch with my grandmother who I truly love and care for. One has dementia and the other has cared for me the most in my life but lives out of country most of the time. So I wouldn't be able to contact her. My mother has done it before. 
We so badly want me to move in together at his parents but we're trying to hold off as long as We can. So we don't have to ask his parents for more help. They've already bought a crib and so much more without us asking. his brother family used to live with them but it was too hard on the parents and he doesn't want to stress his parents out.  The government job pays over $65,000 yearly and goes up with overtime. But again we have to wait till it starts in January