At 16 your daughter is able to choose with whom she wants to live so you are not breaking any laws.
As your daughter is still under 18 and likely to be continuing with full time education - I would suggest that you give consideration to issuing an application under the Children Act Schedule 1 for provision of housing for your daughter. This would last until your daughter reached 18 years old. Such an order would mean that the property would transfer to you on trust for your daughter until reached 18 then it would revert back to your ex partner.
Post 18 - your daughter can make a schedule 1 Children Act claim in her own right.
glad I could help.
First thing to do is refer to family mediation. They may be able to help you reach an agreement without the need for court. This will depend on the mediator being able to speak with your ex abroad.
If mediation doesnt work then the mediator will sign the form for you to send to court.