Picobama
Are you me?!
I have almost the identical problem with my DS, also 9, and he is beautifully behaved everywhere except at home! (Or occasionally at my mum's, but we lived there for a year, and he slots straight in as a younger brother/son more than a nephew/grandson)
I was tearing my hair out (literally) with his behaviour a few weeks ago, and I admit I think it was because we weren't being consistant. I notice that you have more problems at weekends/holidays ... snap! I'm sat there thinking - why are you so badly behaved?! You go out and play for x hours of the day, you don't have homework to do, you choose when you get up, you go to bed a tad later than normal, but otherwise you have no great demands on your time! Stop being such a sod!
After a lot of tears and talking with my mum (I was an absolute brat between the years of 8 and 18, and I still fly off the handle when very PMTish) and DH, we've implemented a time-out procedure, and also we're knuckling down on his daily jobs which he earns pocket money with. (We let this slip during the holidays)
I know it doesn't help that we are a 4 member family (soon to be 5) squashed into a 2 bed house, but at the end of the day, that's how it has worked out.
We have tried to establish that his bedroom is just that - his bedroom. Yes his sister (20mo) sleeps there, but none of her toys/clothes are kept in there, so apart from the cot and her wash basket, the room is soley his.
If he backchats/flips out/behaves inappropriately, he gets one warning. If he doesn't calm himself down/moderate his behaviour then he is asked to move to his bedroom and left to shout/scream/beat up the pillows as he sees fit.
We use one phrase and stick to it - "Please go to your room and reconsider your response"
This is starting to see rewards now, in that he's starting to moderate his behaviour after the warning. He also has made a 'calm-down space' for himself on his top bunk - pillows, favourite books and toys (he came up with that on his own) so once he has started to calm down, he can help himself further IYSWIM.
The only time it didn't work for me was last week, when DD was down for a nap in the bedroom, so he ended up having a full-blown melt-down in the front room. Not a lot I could do about it except quietly stop him from destroying the games console/TV etc.
The trigger? I asked him to handwrite a piece of homework, and I didn't have any lined paper for him to do his homework on, plus my printer had run out of ink so I couldn't print any guidelines for him to use under plain paper.
Once he had calmed down, and was talking rationally, we discussed the situation, how his behaviour had made me give him the warning/time-out (this caused him to escalate), and thus I 'switched off' (this enraged him further)
We discussed the problem, how he should have spoken to me/asked me for help, and then I showed him how he could solve the problem with minimum input from me.
We are far from a permanent behaviour change but all I can do is be consistant!