Moving a nursing mother rabbit and her 5 day old babies

I have posted already about some surprise babies I have from a stray female. They are doing great and they are currently 5 days old. The problem is they are currently in a hutch with a run underneath and it is more or less impossible to section off, as the area the babies are in is far too small to keep mum in full time. I have created a small lip at the entrance to stop and babies from rolling out, but as they get older I am worried that they will fall down the stairs.
I have a large wooden playhouse which could be easily converted to house them all but I am asking advice as to whether this would be wise or the best time to move them all. Mum is lovely and laid back and seems very content with me handling the babies, etc; but I do not wish to cause any undue stress to her. Not sure what would be best for mum and the babies.

Not yet, you need to make that lip as high as you possible can but still allowing mum to just squeeze through, that should give you extra time. When they're getting active enough to need more space or to jump over the lip move them, but personally I wouldn't until that time. You can take mum out and put her in a run through the day to give her extra space. I'd also suggest making a shelter in the run bit of her cage so she can get a bit of rest and have privacy without babies trying to latch on constantly

Yes, I agree, wait until the babies are starting to be mobile before moving them - it won't take them long! I would get the playhouse ready and you could let mum spend some time exploring it so she's used to it before moving the babies in. That way it won't be as stressful for her

I think that does sound the best idea, as it will take me a few days to get it all sorted. I have asked my kids and they are happy to sacrifice their playhouse!
I normally let her have a run in the garden in the day, but she got out when the babes were 2 days old and luckily found her up the road. 5 years I have had my other rabbits have more or less had complete run of the garden and they have never got out, so I am presuming she is a bit of an escape artist and that maybe how she became stray! So I feel cruel cooping her up in a small hutch. My others have a 6 by 6 aviary and run of the lawn.

I have just been looking at some of the pic of housing on the forum (as I am a newbie) and some of them look fantastic and I am going to have a go at producing something like them on the wendy house.

When you suggest waiting until they are getting about to move them, would you suggest this would be about 2 week then?