So, the xfer is from a CM flight to a UA flight. The exact itinerary would be helpful.

But UA has 3 flights to IAH and 1 daily to EWR, right? So the OP is either catching a 9:30-ish flight to EWR or IAH, or a later (12:41, 15:30) flight to IAH. Only the morning flights present any sort of rush at all. The afternoon UA flights are smooth as silk. Unless it's a very early flight on CM into PTY, I think the 2 hour layover is no problem whatsoever, even if the pax has to schlep the luggage out of customs, upstairs to the UA counter, and back through security. Of course it would be better if CM checks it all the way through.

UA will close up shop at the check-in counters upstairs at T-60, so your trip may go haywire if the CM inbound is late.

I have seen plenty of UA-CM bags (and vice versa) on the carousels. I would be fairly confident that CM will through-check your bags, even on separate tickets, although I have never done it myself. I would trust the counter agents vs. a phone agent.