Who has the burden of proof in a child support hearing. I am custodial she is non-custodial but the daughter got mad over disipline and has stayed with mom for 3 weeks. I still have my 20yr old living with me but will no longer be in picture when he turns 21. The non-custodial parent thinks he does not count. Who has to prove the case Petitioner or respondent?

You each state your situation, and you are told what to pay (the court already has a number in mind), end of story. Of course there is burden on you; why would your wife/ex have to prove your financials?
Your over 18 adult child, unless he is disabled and unable to provide for himself, doesn't count, regardless of when he is leaving.
This is your child whose support is being fought over? 'the daughter?' A bit chilling.

You need to go back to the laws of your jurisdiction. Probate and family courts can have wide jurisdiction to order support for even post 18 year olds in certain circumstances depending on the statutes (i.e.: college payments, insurance, etc... ).

Though, I am not really clear on what the situation is and that would likely determine who has what burden.

Generally, the custodial parent is the one receiving a payment for support and if the custodial parent is looking for an increase they probably have the burden to show a change in circumstances. If it is for non payment again the custodial parent likely has the initial burden, then it would shift to the non-custodial parent to show reciepts.

If this is a situation of the non-custodial parent suing for custody (which I think is the case here), then the burden would likely be on th enon-custodial parent to show a change/unfitness etc...

Also, if the non-custodial parent is violating the court order (by keeping the child) then you have an action against the non-custodial parent. That said, be careful here... alienating the child

I am guessing though, can you explain more about what the situation is?