A home where your mother is degraded, emotionally and verbally abused, is no home a child wants to be in. Do you want your daughter to grow up learning that this is how men are supposed to treat women? She will repeat this pattern when she grows up if you don't do something.
Unfortunately, it sounds like he went for someone so much younger so he could have someone to control. Do you have family or close friends you can stay with? Maybe you two can work things out in counseling, but until then, you need to get yourself and your daughter to a different environment. Nothing is going to get better while he has control over you. If you are afraid of him, then you really need to get out.
As for custody, he can't take your daughter away from you completely. Yes, he can have joint custody, but unless you are an unfit mother, the courts will not take her away. Just make sure to get yourself a good lawyer.
Please write back and tell us how you are doing. Good luck.