We have dsd every other weekend. It was every 3rd weekend as per Court Order but dsd asked to come more often. In addition she comes for half of the school holidays. It was supposed to be 2 weeks in the summer but again when she got older she didn't think this fair, so asked to come for 3 weeks. We are supposed to have her from 10 am Boxing Day for a week but she has asked to alternate Christmas with her mum and her dad, so this is changing too.
Dh used to have to meet his x in a car park. She didn't want him going to the house (long, complicated story but to do with her then partner, not because dh was aggressive or anything like that). It was horrible. After the partner left dh started going to the house and gradually as the ice has thawed with his x he has graduated from having the door closed in his face and dsd eventually coming out, to going in for a quick wee to now going in for a cuppa and a chat - and last week going in and providing a shoulder for her to cry on!
Dsd is delighted that her mum and dad can now be in the same space and be civil to one another (and it was never for want of trying from dh's point of view), and it's stopped dsd being able to play her mum and dad off against each other as they now communicate.
So I'd say that the best thing is for him to collect from the house - but he doesn't have to come in if that's difficult for you, he can always knock and wait in the car.
Dh used to have to do the take her out for the day thing. After she ended their relationship, his x stopped him seeing dsd, so dh went to Court. His x tried to say that dsd didn't want to see him and wouldn't know him, all sorts of excuses, so the Court ordered that contact be built up gradually. The Sundays spent in a town he didn't know, with little to do on a winter's afternoon weren't the best times he ever spent with her. They were special, of course, as he was seeing her, but we did used to end up in a Brewster's or Macdonalds just trying to while away the last hour or so, having been to the park, swimming or cinema. It really wasn't ideal.
What was far better was when dsd was allowed to start coming to our house, and we could just do normal family stuff. And when she started coming for whole weekends it was even better, not just because dh got to see his little girl more (he missed her terribly) but there was time to do things like swimming or the park, plus cuddling on the settee watching videos, having a family meal or playing games with her. Just all normal stuff.
I don't think coming in to put them to bed is a good idea, but he must miss them and they must miss him, so I can understand why he might want to do it.