No, do not force her. She clearly knows what she wants and is old enough to express her wants and her reasons for them. Respect that -- you are respecting it already but someone else in your home isn't....
Why is your husband so invested in forcing her to do something she clearly does not want to do? Is it really also about forcing YOU to bite the bullet and put up with someone he believes you should just get along with, namely, the coach? Ask yourself, does he, in other cases, also want you and/or your child to do things he knows you don't want to do -- just so he can prove some point of his own (that you should be tougher, that your daughter MUST be in an organized sport "like other kids," etc.)? Think it over. I really wonder about dads/husbands who insist on children and wives doing things that they have clearly and unequivocally said are not for them. I think it's about more than one sport -- at some deeper level it may be about the dad himself and his own need to have a sporty kid, or a wife who doesn't "cave in" when he thinks she shouldn't. Don't let him bully you or your child on this.
You already dropped one individual sport. I don't see how a team sport, where she says she is not interested, is going to work. She will be miserable; you will be miserable; her schoolwork will suffer, since you're already struggling to keep up; her need for down time will grow greater, not less, if more of her time is burned up in an activity she dislikes. If you must, put it all on school -- Does he really understand that schoolwork is already a struggle?
If her real friends are on the ball team and your child was very eager to be with them, she would have said yes to the team! So I'd question whether she is burning to be with these friends anyway. Clearly she knows herself well enough to know that even WITH friends on the team, she does not want to do this. Nothing could be clearer than that. Once a week to play actually is pretty darned good if she has a demanding school load; my daughter doesn't even get that, between school and her activities. So please don't let the social aspect sway you. Listen to her. And get your husband to listen and respect her and you, as well.