Kid not going to sleep alone after divorce

My kids mother and I have been divorced for a little over a year (the kid is 4) we split custody 50/50, 2-2-3 schedule. Getting the kid to go to sleep has become more and more of a challenge.We have a routine of bath time, pajamas, brush teeth, read books, a little bit of snuggling / rubbing back, and then going to sleep. Soft jazz plays while she sleeps and she has a harem of stuffed animals on her bed.When I give a kiss goodnight, there is always a lot of protest. Sometimes it is "I'm hungry" (mom lets her snack in bed, I don't) or "I feel sad and alone when you don't sleep in my bed" (mom sleeps in bed with her, I don't), "I miss mommy and want to be with her". Kid leaves their bed consistently throughout the night to tell me that they feel sad without me in bed with them. If I'm lucky, and they fall asleep right away (rarely ever happens), they sleep through the night fine. But more and more recently it is causing the kid to stay up later and later and getting less and less sleep.The first successful strategy I tried was telling them that I will come back into their room later to rub their back some more, I would head downstairs and come back up half an hour later to rub their back 9 times out of 10 they had already fallen asleep.But increasingly this isn't working. The kid won't fall asleep, leaves the bedroom to tell me they are sad/hungry whatever, which take repeated attempts to get them to go to sleep. There seem to be plenty of nights where I fall asleep before the kid does.I'm worried about the kids lack of sleep. I'm worried about the anxiety they may be feeling at bed time (I don't want to exasperate any feelings of abandonment).I know the different routine at mom's house (staying up later, eating in bed, sleeping together) may be a part of the issue, but I can't change that and I don't want to match that routine at my house.Advice? via /r/Parenting http://ift.tt/2fL4efR