I agree with several peoples points.
1 - This is not a good situation.
2 - If you are the child's father, you need to be acknowledged as such. Sit down with the child's mother and her parents and establish those roles right now. I am dad and this is mom and what we say goes. They may tell you to get out.
3 - If you are in the U.S. it is not necessary to get married. If you want the child and mother to be your dependents, you need to be married. Insurance will give you such hell it won't even be funny.
4 - If you want strict control over the situation, then ask the child's mother to move out with you and find a way to do it, money or no. If you do not you will continue to receive a frontal assault from grandma and grandpa. Every time you turn up it will be a new battle you will have to face. If you give in, just once, you will be shoved out of your dominant position as father figure. Mom is probably being challenged every moment she is living there.
Spanking is up to you and mom. I found it easier to hold up my son to my face and give him "the look" straight in the eye until he looked away.