Questions on taxes relating to claiming a child.?

My wife and her Ex-huband have joint custody of our 8 year child. My wife is the custodial parent and the child spends more than half the overall time at our place. Over the last sereval years, we will take turns on claiming our child (One year us, the next year her ex). Keep in mind that we aggreed to this and signed the diclaimers for his years to try and keep thing a 50/50 split. However, our tax person said that new rules may be coming down soon which will require that the custodial parent claim the child. I don't know if that correct, but it's headache of trying to figure out stimlus credits and rebates every year. We were going to propose a annual monitary amount to her ex if we can claim the child every year. Is there a way to figure out a good ball park amount? I know that this affects the taxable income, but if I have someone's yearly income, should I be able to figure out their refund both with and one without claiming a dependent child? Then what ever that amount is, we would give him half. Is there a way? Thank you so much.