TM moves don't pass down at all anymore as of this generation, presumably because that would give a massive overkill considering egg moves now pass down via both parents (so that the offspring would quite often try to inherit like six moves if both parents know a fair amount of TM moves) and because TMs have infinite uses anyway lol. If there are still more than four egg moves to inherit, I THINK the female's have priority, but I'm not sure and Bulbapedia doesn't offer any help; however, I know for certain that there is some kind of priority involved, I just can't remember where I found it when I first looked into it :D.