A word that is more definitive of this particular type of adult relationship? Ok how about……marriage? Why is this so important to you? I’m not being a dick here. I’m really trying to get to the root of why you feel same sex unions can’t use the word marriage. You say it’s not religious but I can’t think of any other reason.
Your mule horse donkey pony analogy leads me to the conclusion that same sex love is different and not worthy of the word marriage? Ok that’s fine. But why? How does this affect you? Why do you feel this way? You’ve not articulated this at all.
EDIT: how about this. If you have a problem with same sex unions being called marriage. That’s fine. Call it something else. Call it a union, a partnership whatever. But also let them call it whatever they want to call it. It harms no one.