OP, this is a really difficult situation, seeing as how your mom is so very manipulative and controlling.
It looks to me like a big part of the problem is that you are an adult, and she is treating you like an infant or very small child (which is the only time it is appropriate for a parent to be totally in charge of the child's grooming). Boundaries are supposed to change as you grow up.
The difficulty is that you are seeing your relationship with your family as dependent on putting up with your mom's crazy, because that is the way the situation has always been. This is an illusion, and it is one that your mom wants to keep, because it is her leverage to control you. Every time you go there, you are putting yourself in a dependent position, which just reinforces her treating you like an infant.
I don't think that continuing to go stay in their house, and blow up or arm-wrestle with your mom to enforce your physical boundaries, is healthy for you or for her. When you are free to stay or leave, then you will be free to accept (or even offer) sincere affection because you will not feel coerced.
There are many alternative ways to build and maintain your relationship with your family, but it will mean changing the frequency, duration, timing, or other circumstances of your visits, or communicating with them directly through other means. Your mom does not own your father, or your grandparents, and she cannot take them away from you. That is part of dealing with your mom (and your family) as an independent adult, separate from her. You can't, in essence, "use" your mom to serve your emotional needs (visit with relatives), and expect her to not "use" you back to serve her emotional needs (inappropriate grooming)
Hugs (of the virtual kind) to you! I really hope you are able to move forward with this and things get a lot better for your relationship with Mom and the rest of the family.