L.A.
This is a tough situation. First and foremost, you, your husband, and her mother need to be on the same page about discipline. Guidelines need to be set, and everyone needs to follow through with them or else it's not going to work.
Divorce or parents that split up, whatever the case might be, can be hard on kids as is, but as adults, your husband and his ex need to realize that they are forever connected by this child, and they are doing her a great disservice (IMO) by not giving her any structure. They don't have to be the military, but there has to be guidelines that are the same, and are followed, at each house.
You say when you ground her you can't make her mom enforce it...well that's not how it should be. If you give her punishment, mom needs to let that stand. If that means you sit down, and you make a list of the things she does that are wrong, and then write down appropriate punishments, then you do that. If something comes up that is not on the list, you come to an agreement that until you can talk to one another, she is to remain in her room, no tv, no phone, no computer or something of that effect.
I know raising a kid between two homes must be difficult. But until the three of you, especially your husband and his ex, get on the same page, things will not get better.
If some of this didn't make sense, please message me and I'll try to clarify. I hope some of this helps.
Good luck!