With your daughter being 16 years of age if she doesnt wish to go then she doesnt have to. No family court will do anything about it as shes too old now for an order to be made.
Same with a child arrangements order , you could have your kids a lot of time when they are young. However once they reach their teenage years contact sometimes becomes a lot less as they are doing other things in life. They probably hardly see their own mum either. As a dad its potluck how long your kids see you on a regular basis once they hit teenage years and impossible to predict when they are young.