I think you can't force independence. It comes when they are ready and you can kind of help them along the way, but it needs to be gentle. If it is forced it could completely backfire, often by nurturing closeness when they need it you will get that independence later (Pinky Mckay has written about this)

The first thing that needs to be worked on is the bedtime, it is really quite late as Pandora has said. Good idea to have a similar bedtime to what she has at home. At least getting her to sleep by herself for those few hours is the first step to getting her to sleep by herself the whole night. I understand you need for adult time of an evening, I certainly have that need as well.

As for spending the whole night separately, well there many dads who are shift workers, or who work away, so I see a dad spending time with his daughter a few nights a week not to be such a bad. I think if you can get her to bed earlier, then things will be better.

My 5 1/2 yo often wants to come to bed and sometimes still need us in the middle of the night. So I think it is quite normal for a 6yo to still need a parent to some extent of an evening. I suppose it is just finding that workable balance.