Wow - you've had some harsh comments in this post - and not entierely fairly I don't think. You've not suggested that you're mean to his DC in any way, just that you'd like some time without them.
I'm in a very similar possition to you (DCs with me in the week and alterate weekends, DP has his DCs every weekend - so I stay at his on my free weekends), and DC are similar ages to yours. I do like being around his DCs, and am about to move in together. But do completely understand how it feels to have very few times together without the DCs. I also do the same as you of sending (or at least encouraging) mine off to bed and having some time together in the week, but then finding his DCs in control of the telly til after DP falls asleep on the sofa at weekends....
However, I do think that if he wants to have his DCs every weekend, and his ex is happy with that (always puzzeled me a bit why DP's ex doesn't appear to want any weekends at all with her own DCs.... but probably not my concern) then it's probably not on to try and alter that substantially.
We have come up with a few compromises that work for us though. These include a weekend or week away a couple of times a year, and a few odd days together child-free too (when he takes them back Sunday am rather than evening). We've also drawn up some better house rules regarding the telly and bedtimes - so his DCs are now off to their own rooms by 10pm (ish). This helps a bit to get us some adult time together whilst the DCs are around. I've also pushed the issue of going out in the evenings together at weekends and DP is now OK about leaving his alone sometimes (if your DP's eldest is 13, would this be a possibility for you sometime soon?) DP is also completely alright about me taking some time out of the weekend so I often go out to see friends a bit, and come back to his to sleep. I don't feel under obligation to be with him and the DCs all the time.
But guess at the end of the day only you can decide whether you would want to move the relationship on as it is at the moment. As I said, we're not yet living together so I can't tell you how that feels, though would imagine that if you find the DCs hard now, you would find it harder if you were living with them.
Could you prempt him proposing by saying that you would like a long term future together but would prefer to keep two houses until the DCs are left home? - or maybe til the youngest is teenage and off having her own social life a lot more?
The sitting on your lap thing is probably her testing boundaries - if you're not happy with it, then just say "oh you're a bit of a heavy lump for sitting on my poor squashed lap, here [shuffle up couch] sit here instead" or words to that effect. My DD does that sort of thing with DP, checking out how close she can get to him. It's up to you to decide what you're comfy with - and if you feel you can't lay down boundaries that you're happy with at present this could be one thing that is making you unhappy around the DCs.