That's hard!!! I have kids the same age (13,just turned 10, and 6). so I know what you are going through! My older son is the only one that ever really gives me any trouble. He went to christian & then public school for K, 1, and 2. He does have days where he is not into it at all---and I have told him the same thing:"U wouldn't talk to a regular school teacher like that! DON'T do it to me!". First off-make sure your hubby is there to back you up!! Keep up with what he says/does and have your husband call in from work, or maybe surprise him by coming in during school time one day. If he knows there is someone besides you, he may try a little harder to be respectful.
I think some of it(Just a tiny part) is their age----Lord knows the hormones and changes that run through a teenage mind/body!!! Do you think that could be some of it? Some times i just have to send my son to his room, or out for a run to get him focused. Also, I have to make sure he IS challenged enough--my boys are also well above 'grade level' so lots of their work is from a grade or 2 above their age. This has really worked out well. Challenge is a good thing! Not too hard, but certainly engaging.
How long have you been hsing? Maybe they just needed some down time from ps. If not maybe he needs some encouragement/incentive. Four days a week and a 3 day weekend...An extra hour with a game he enjoys....take off early one day if they are participating and behaving and go out for lunch or a movie!! Make him see that they have advantages that ps kids don't get!! My kids are mostly finished with school by lunch--then we go do things while the other kids are in school. That way we can enjoy things like an empty theatre!! Or shopping for needed tennis shoes without a crowd of people. Their favorite thing is to go spend the remainded of the day with their daddy at work! On days when he can, he takes one, two, or all three of them and I get a much needed break!!!
Do they like to read? I am a big pusher for good literature. They should have their own library card and be taken often. We usually do the summer reading program at the library, then continue it for the rest of the summer at home. Every so many books gets you a bigger and better reward. Great books are a way to fill empty time....if they are finished with school/chores and still you have attitude problems, send him to read for so much time, or so many pages. They must be able to narrate or dictate to you what they read. It really helps in all areas-grammar, concentration, comprehension. But don't only do it for when he is acting wrong-make it part of your daily activities, but more time added for if he isn't behaving.Or an extra book for that. He just needs more of something to do! It could even be housework for you, or cooking...anything to keep him from being idle. And the longer the rotten attitude, the harder and longer the chore! If the attitude continues, you and your husband will have to decide where to go from there. Maybe he needs to speak to your pastor or someone your trust about how he feels and the changes he has gone through--in himself and being brought home for schooling. We all need people to listen to us at times!!! Hope this helps a little bit!!