If the property is in your cousin's name he can throw you all out anytime he likes because legally he owns it. I doubt your cousin will sign any deed of sale even if you asked him to as he knows that he is the owner of the property now. You entered into a bad arrangement at the front, buying it in his name and now you are stuck with this situation.
Lets hope he does not throw you and your mum out.
Your cousin owns the property and, yes, he can make you move. It doesn't matter that your mother is making the mortgage payments.
She cannot transfer the property into her name unless your cousin agrees and signs the appropriate paperwork.
If you're in the US you can't force your cousin to transfer the home to you.
It does not matter who is paying. The house is not in your mothers name and never will be without the permission of your cousin.
We are living now on a property that is named next to my cousin. The property is not yet fully payed. We just used his account to the Pag-ibig fund but we are the one who's paying the monthly amortization of the property. Can anyone advice me what to do in able to have a proof that we just used his name and we are the one who is paying the property monthly? Because we are afraid that he might took the property to us. My mom is the one who is paying the property. Any suggestion?Please help I needed an advise