I think you need to talk to someone about this, would she go to a family therapy session with you and the boys to try to iron this out? I know that families have differences of opinions (my mom was married 5 times, so I've dealt with quite a bit of what you are talking about) and it's very, very confusing for the kids.
What concerns me most is that the kids are being *punished* for things they are doing at your house. I think this needs to be documented and addressed. I like Can'tDecide's suggestion of trying to come to some written, formal agreement, however, if she doesn't play ball because of her anger, it's going to be worse in some ways.
FWIW, if your kids are comfortable with watching those movies (not asking them to be turned off) and you are not forcing them to continue, then I'm not sure what the trouble is. It's sad, because they are going to enjoy her less and less if she makes these hard lines with them. I mean, I'm all for caution, much as you are, but this sounds a bit like infantilization to me. She's treating nine year olds like kindergarteners and they are going to eventually rebel. I hope she can get some help and move forward in a more secure way, otherwise they may just become angry with her.