Can a parent who is paying child support (father) ask to have to other parent (mother) pay instead of them?

Yes, if dad gets custody of the child, he would be owed child support from the mother.

Why are you seeking custody? Is it because you are behind on your child support or tired of paying it? If that is the case, it has been tried before. Judges are on to you. You will be wasting your time.

The courts are only interested in what is in the best interest of the child. It doesn't really matter what dad, mom, or even the child wants. It is in the best interest of the child to be raised by the better of his two parents and to have healthy relationships with both.

Nobody can really answer this question unless perhaps said person is a judge or lawyer. Even then, they can say for certain yes or no. But to answer your question: in my own experience with court, if the custody changes then the child support will more than likely change as well. If they have joint custody, I'm not sure if either one should be paying child support. If the two parents are sharing custody, as in one parent has residential primary care while they share joint decision making, the child support then goes to whomever the child is living with. Again, this is not for certain as I do not know the circumstances. I am not a lawyer, judge or otherwise employed legal representative. This is purely from my own experience.

It depends where the 12 year old lives if the 12 year old lives with the mother then the father has to pay the child support. Or if the 12 year old lives with the father full time then I guess the mother would be responsible in paying child support but other then that no other way around it.

It depends on who the child lives with. The custodial parent ( who takes primary care of the child) is usually the one who receives child support. The non-custodial parent pays for the child's care. If you want the situation reversed and the other parent to pay, then you would have to take primary care of the child until age 18. Get an attorney who practices family law to give you advice.

The only way a judge is going to order the mother to pay support is if you have/get custody

And even then you have to be up to date on your support payments

Both parents need to pay for their child. Both are on the hook until the child is 18, no 2 ways about it.

mother is the primary parent. the 12 year old lives at mothers home five days a week and is at fathers home two days a week.

No. Unless she lives with the father full time. Been in and out of court with baby daddy for years. Heads up, judge usually sides with mother. May not want to hear it but its the truth.

Depending on who is taking care of the child full time

that should be talked at court then asked on here cuz its kinda a legal issue of parents.