That's an odd problem. I'm not sure what it could be. Did it do it before the rear brake install? Does it have a proportioning valve? Maybe the stock proportioning valve isn't right for the rear discs which is basically making only the fronts have any real braking power. I don't know, i'm just thinking out loud.
As for the tire, i dont know about those particular tires, but as long as they aren't all out road racing tires they shouldnt be the cause. I've ridden in alot of Mustangs with wide tires and it wasnt that bad in the rain (although then again they didnt help either)