Y.C.
I feel your pain. My daughter is 2.5 and she has being waking up in the middle of the night for months!
She doesn't sleep during the day since 5 months ago and she still waking up in the middle of the night.
Sometimes when she sleeps with a diner full of protein she sleeps all night but is not always.
I would give her a nice diner like chicken, rice and broccoli, not much just little.
I also would put a night light.
If this doesn't work I may try the cry out loud but I also would be open to co-sleep with her. I am not big fan of co-sleeping because both moved "a lot" and neither of us could sleep, but in your situation maybe is an option until you are totally settle.
PS: I would bring some cookies to the neighbors, if they have kids they will understand.