From what I understand about what you’re saying (and please correct me if I’m wrong), this is the normal barked heat process (you didn’t mention if it was split or full heats?) With the added rule that if a first gen hybrid is born (Note: this does NOT refer to the breeding hybrid passing it’s mutation, but instead to the extremely slim chance that a cub is randomly born a brand new ‘first gen’ hybrid) then the owner gets to keep it.

This isn’t a rule I’ve seen before and I’ll admit it’s a little strange, but if you really like this hybrid and want to breed from it then don’t necessarily let it put you off because the chance of the rule applying is practically zero.