Don't feel bad or other when it comes to your daughter. Accidents happen, however, if they hit, bite, scream at, ect.. your daughter, get her the hell away from there. She will learn. She will mimick everythings.
If it's just your MIL's parenting style then, that may not be fair to keep her from her, however, as you stated, sounds to me that there is more.
Tell your MIL I was adopted and it didn't give me a reason to run rampant and attack others and get away with everything.
I have very different issues with my in-laws including lack of trust to abide by my rules or to adhere to the saftey issues I have for my children. Mine are very different than yours however, saftey is just that.
You should look at it as your job. If she gets mad at you, then so be it. I have told my husband, even when we were going through a nasty divorce that it is 100% my sole responsibility to protect my children and care for them, even if they are not with me. Because the courts will look at wether or not I knew the environment I allowed my children in. Ect..
Hope that helps. Be confident in your decisions and don't worry anymore about hurting anyones (your MIL or husbands) feelings. I've been there and you know what, my husband finally saw the light and agrees with me.
A little insight: My MIL raised (had custody of) her daughters baby for sometime (she's 12 now). So when my children were around her, she felt like she became the mother and whatever she said went. Yea, that didn't work for me.
J.
p.s. all of our husbands are childish to some degree, so don't feel bad. lol
p.s.s. My husband and I decided not to divorce