Hi there
I wouldn't beat yourself up about sleeping with her, if my family had been through so many changes I would have done th same if my DS had needed it.
I see you've only just moved into your new home (congrats), is her room all set up nicely now so she can feel comfortable in there?
Can you spend some time which is not BT with her playing in the room, putting laundry away, getting some toys out, having a wrestling match on her bed, playing hide and seek (just hiding under a blanket or whatever Whispering things like "she'll never find me here")... this can all help a LO get used to their new environment much faster and associate it with nice things they've done with mummy or daddy.
I would get a night light if she wants one on, try not to get blue light as it can disturb sleep.
My DS used ot sleep in total darkness but eventually went through a very long phase of wanting a small night light left on. I just let him have it (ours is built in to the sound monitor). After sleeping happily with the light for ages we eventually came to a phase where both DS and I worked out that the night light disturbed his sleep in the early hours of the morning, as though he though the sun was coming up. For another long period I left the night light on for him to fall to sleep and then at my BT I went in a turned it off so it didn't disturb his night sleep. The current phase is that the light is to be off when he goes to sleep (just like years ago) because he wants the room properly dark again... so we'd have every possibility and it just changes with developmental phases.
I'd set up a bed on the floor for yourself because really you are going to get through this much faster if you don't resort to taking her into your room. If you are near her on the floor you can verbally reassure or reach a hand out to her when she wakes and you might not sleep well at all but you can at least doze between NWs. I did this when my DS moved rooms (not cities!). I was shattered for a few nights but things moved on quickly.
NWs are normal, even adults NW about 5-6 times per night as we transition from one cycle to the next, the goal is not to prevent any NW but for her to be confident enough that when she comes to light sleep and wakes she just goes right back to sleep. Initially I'd say that to build her confidence would be to know that you are there, she doesn't *need* to fully wake and call out but if she does you can say "I'm right here, everything is okay, go to sleep". I would imagine after a few nights you could move out of the room and sleep in your own bed if it's not too far away and can use verbal reassurance, same/similar phrase. If not though then a more gradual process of moving out of the room might be needed (I'd go with the more rapid move out of the room myself).
For independent sleep at BT I would just stop laying with her. have your usual wind down, books, cuddles etc and then move to by the bed not on it. Sit on the floor or a chair/stool and be close enough to have a hand on her and just keep on repeating that you are right there, it is time to go to sleep. Let her go to sleep the first couple of nights with a firm hand on her if needed but then reduce pressure and within a few days more have the hand off.
The thing with this sort of gradual withdrawal sleep training (or re-training) is you need to keep on moving forward, always helping but also being relatively firm about the gradual move away. When you reassure have a confident voice, you know full well she is in no danger and that you will return to her if she needs you so let that be heard in your phrase so that the confidence is passed on. Sometimes I think a confident instructional tone is more confidence giving than a soothing pacifying tone (they are both loving and caring).
The nap at daycare might not be working in your favour. She could be UT for her night sleep and this will cause problems with sleep training and length of NWs (because she has the energy to just keep on complaining or calling for you at night) but I know some daycares will not stop napping kids. Maybe ask if it's possible but if not then you just have to deal with what you've got.
Hope this helps some
