Aaliyasmum, as far as telling off SD try to take a back seat for a little while until your SD gets used to you but don't be a pushover either if your SD is doing something that you don't like say something along the lines of, " Could you stop doing that please darling" then your DP should re-enforce that by agreeing with you, or you could take your DP aside, talk to him and when he says something to SD 'second' him to show your agreement.
Your SD needs to know that there are set 'rules' in your home, they maybe different to the rules she has at home, but after all there are rules at school, rules when they visit Grandparents etc, why shouldn't there be rules in your home?
Your home should feel like 'home' to your SD but she should respect your rules. You should discuss these 'rules' with your DP beforehand and present a 'united front' if the situation arises.
I know my SD tried to be sneaky and do things that she knew she wasn't allowed to do then if I said something she would say "Daddy said I could" and visa versa. So we had to really talk to each other about behaviour/things allowed/disallowed, and in the end DP said to SD (after her trying it on again) "Look we (DP and myself) do talk to each other you know, we know what you are doing".
AS for the x trying to tell you when to put your child to bed cheeky moo!!! You do what you think is right, do not allow the x to dictate your life.
I hope this helps, keep posting to let us know how you get on.