Blaming things on Izzy isn't exactly a horrible move, but the way he's doing it is overkill. You need to pick and choose what you deflect to her, by throwing everything there just makes it look obvious that you only blame her because she can't defend herself. If you own some of the smaller shit, it makes it more plausible and actually builds yourself some trust.
The problem with them and this stupid alliance thing is that they think they need to cover all bases by having enough members to be the majority of the house. They're far enough into the game that they would be fine with a 4 person alliance. Especially while their side is in power.