I am going to be a minority voice here!
Is it possible that your DP has a legitimate point, perhaps not very well communcated...?
From your post it is clear that you feel as though he dislikes your daughter and is overly critical, also that his expectations of behaviour and discipline are different from yours. I think this is pretty common, and I have already seen a bit of it on other threads here - but from the other side.
You say that you only believe in restrictions when DD totally messes up - from your DP's side, this might feel like a lack of appropriate discipline (I am NOT saying that it is, I don't think there is enough information in your post to begin to even guess that, and I wouldn't presume to say so anyway - I am just trying to see it from the other side.) You say he dislikes DD because he criticizes and argues with her - he might be surprised by that, and feel like he is just trying to have some rules in the house that everyone can live with.
For instance - My stepkids also take two busses to get home from school - but I still expect them to do their chores when they get in. They don't always want to, and my SS will argue that he is too tired, or has no time to play, etc, etc... (I should point out - the kids have a great deal of leisure time, and their responsibilities are pretty small.)
My DH would be a bit more sympathetic to SS's viewpoint than I would, both because of our own childhood experiences, and because of the 'DisneyDad' syndrome. No matter what, he would have been a more laid-back parent than me, because that is his personality, but because of his feelings of guilt and compensation for the kids, it is exaggerated. I am by no means strict, but I do have more of a belief in rules and consequences when it comes to kids.
I really don't mean to sound as though I am taking your DP's side. I have no idea. But I can see how his view of things might be quite different. A lot of the replies are telling you to get rid of your DP - but honestly, I am not sure how anyone can say that based on the amount of information in your post. I do think some outside help is a good idea. You might also want to talk calmly with your DP about what are fair and appropriate expectations for an 11 year-old. Maybe his are too high, maybe yours are too low, maybe there is a middle ground that would be better for the whole family.
SOrry if I am out of line.