It sounds like what we do with DS might work for you (though we never had as much trouble with him re tantrums etc - but still, think it would be worth trying).
You would need a stairgate at the top of the stairs, and a bolt or hook on the outside of any other upstairs rooms you especially want to keep her out of or which might be too exciting.
With DS, we do his bedtime routine, finishing with a story of his day, for which he has to be in bed (or he doesn't get it). Then lights out in his room, but he usually asks for the landing light to be left on and his door open so he can see a bit (no problem). Make sure lights are off in any other upstairs rooms though, at least until she's asleep. He also has most of his toys downstairs, and only books and a few jigsaws in his room.
I then say night night and head downstairs, closing the stairgate. However he IS allowed to get out of bed, and do whatever he wants (within reason, not too noisy etc) in his room. If we notice he has come out to the landing or gone into other rooms (i.e. if he is being a pain there or might wake baby!), we come up, say "bed" and steer him back to his room but without big fuss. If he is quiet though, we don't come and check he's in his room but just leave him to it.
Usually, he will get out of bed when we go (unless he's especially tired), look at his books/jigsaws for a little bit in the light from the doorway, and then HE will decide he's tired, get into bed and go to sleep. If he is playing for a really long time and won't go to bed, we might eventually switch off the landing light (can do it from downstairs, so no need to argue about it with him) and then he usually gets in bed.
If he shouts because something is wrong, e.g. needing a wee, we come up, deal with it as boringly/quickly as possible and then disappear again. But if he makes a fuss when there is nothing really wrong, he just gets another "night night, sweetie" and I head straight back downstairs, so there's not much incentive to keep doing it.
Think it helps that he feels he has control over when to get into bed, and also that we make everything else as boring as possible from bedtime onward so he is effectively "bored into bed"! And we've never yet come up and found him asleep on the floor with his books or anything 