
Not sure what you mean by a 'travel crate'

Maybe something particularly small or the airline type solid boxes?
Any indoor crate IMO needs to be of sufficient size for the occupant to have room to stand up without having to lower the head, turn around comfortably and lay down at full stretch plus, if being used for more than
very short periods, be more of an enclosed 'pen' rather than crate.
As for crating during seasons, this is not a fool proof method of avoiding a misalliance - bitches have been mated through cages before and no doubt will in future. Ideally, it's best to keep the different s@xes apart entirely in the household using double barriers such as a baby gate on each of two doorways the dogs may need to use.
If using an indoor crate for short term periods is essential and the uncrated dog will have access to the same area, then IME it is better to crate the male than the female to reduce the risk of accidents through the bars! Moreover some males will settle easier if able to still see the object of their desires rather than being kept entirely segregated if they're used to playing 24/7 at all other times :)
HTH, Teri