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get a residency order in place and quick! Then get the contact order started. It will hopefully work out for the best of all three of you in the long run.
Your daughter will probably be encouraged to stay over night, but your ex will have to be deemed fit to have her over night and that will take awhile until he gets the go ahead.
If you are being flexible - excellent, but still get this in the contact order and make it known that you understand that travelling will sometimes prevent your ex from brining your daughter on time, ask for your ex to make sure he lets you know if he is runing late - other wise you will call the Police. Hopefully, you wont ever have to do that, but it might frighten your ex enough to make an extra effort.
Good luck
Flower xx