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Now I would like to have my daughter's mother take her for about a month and a half this summer and she is not wanting to do that.
If she (the mother doesn't want to take the child) you do not have any recourse - you can't just dump the child off and abandon the child with her. That's even though she is listed as the primary custodian.
No, you don't have to give her any support - your the primary custodian and have been since April of 2008. You should have filed a motion for modification of child support way back then so that she would be paying you rather than you paying her.
So, you should immediately file for a modication of child support. You are the status quo regardless of what the custody order/agreement states.
No, the court cannot mandate that a parent fulfill their custodial obligation. What the court can do is place the child(ren) in foster care, refuse custody/visitation for them in the future for not wanting the child(ren), etc.
So, I would gather evidence (documentary, recordings, etc.) that she refused the custody, that you have had the child all this past time, and then go after her for support.
Additionally, the court can make her pay (pursuant to the support guidelines) whatever it would cost to provide other shelter or accomodations for the child(ren) if they would have to go somewhere during this time period.