Decided to rewrite the entire answer so you can be sure of what I said
Yes, this is a case for the Family court
The Family court is a lot less formal than most courts and they try hard to see both sides of the case.
But I have to tell you the Family Court has only one option open to it.
That is to do 'Whatever is in the Best interests of the child'
No other decision is available to it, the child's best interest overrides ALL other concerns
It is for the court to decide in consultation with all parties what those 'best Interests' are.
There are no 'rights' other than those of the child.