Could he just be testing his boundaries with you? If he knows he won't get away with doing it for mum, then he won't do it, but with you he doesn't know that you won't put up with it, so sees how far he can push you.
This is just an idea. Have you tried setting very firm boundaries? If he even starts to hit or bit or whatever, put him in the 'naughty corner' (or whatever your daughter uses to enforce discipline). Every single time. He should quickly learn.
This happens with my son a lot - he learns a new 'naughty' behaviour and will keep doing it and doing it, but after a couple of days with more time in the corner than out of it, he gets the picture! When 'releasing' him, I always get him to say sorry, we cuddle and kiss and I tell him I love him, but I don't like when he hits/bites/throws etc. I don't want him to think he is a naughty person, so I place emphasis on the action being bad, but he is good.
Ask your daughter what she does for discipline if he is naughty - consistancy is the key with little ones!
Hope this helps
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