do you have to let the mother have vistition if she doesnt pay her child support and if she has cat after the dr. said a number of times that the child CAN NOT be around cats...

you cannot deny her court granted visitation legally without taking this back to court

for any reason. BTW, the only issue that will be relevant in court will be the cat issue. Nonpayment of support does not have any effect on visitation except in 1 state that I know of, and that is not OK. (there may be a couple of more, but if so, I haven't found them)

doesnt the cat issue count as harmful to the child...

doesnt the cat issue count as harmful to the child...
Yes, it does. However, to keep from being in contempt the CP needs to first file for a modification of the visitation order, allong with a motion for temporary relief asking for a temp order for visitation ouside of Mom's home. Until a court orders otherwise, the CP MUST allow visits or be in danger of losing custody.