And we don't actually have to get Nohon on our side with those colonies, we just need to back up Nohon's claim to the Mahaxian colonies. Could be something as simple as adding a clause into the peace treaty that gives us control over their Kyberian colonies that reads 'In exchange for sole control over Kyberia, the Dual Monarchy recognises Nohon as the sole claimant to the following territories in North Mahaxia.'
Problem is that this would sour relations between us and the UPM, and doesn't guarantee that they would be able to hold on against the UPM. Conquest
is fair game in this time period, so saying that we recognize their control over that land isn't too much of a barrier. And if the UPM do succeed in their conquests, it would leave us with an unfriendly great power that could mess with a lot of our trade and diplomacy if it wished, not to mention becoming a fearsome foe in the future.
We honestly are unlikely to really be able to intervene in force there. Mahaxia is just too far for us to reach any time within the next century, which means we should assume that the UPM is going to become fairly powerful barring some sort of disaster. That's why I recommend either creating strong ties with the UPM and working with them in the future, or trying to keep Not!Mexico strong and united, so the UPM can't carelessly intervene against us due to a strong nation on their border.
tl;dr We have to be careful to keep in mind that Mahaxia is a very distant territory, and as such our power is very limited there. We can't turn the tide against the UPM easily, and it might be dangerous for us to even try.
Edit: Like, the Mexican American War in the OTL should show how this would go down.
US: I'm not touching you~
Mexico: Your finger is literally a half centimeter away from my nose. Haven't you even heard of personal space?
US: Yeah, but I'm pretty sure I'm not in your personal space.
Mexico: Yeah, you are. *Brushes finger away*
US: OH MY GOD! ASSAULT! I'M BEING ASSUALTED! HELP, MILITARY, MEXICO JUST ASSAULTED ME!!!
Mexico: The fuck? No, I didn't--
US: Come to me, US Military! We must vanquish these dangerous criminals!
*50 burly, heavily armed men appear*
Mexico: ...
*Looks behind him*
*20 pale, skinny dudes, kinda armed*
Mexico: Oh shit--
*1 severe beating later*
Mexico: Stop! Just, stop! Don't keep punching me!
US: Well, I guess you look like you won't assault me any more. Fine, just pay the fine, and I'll stop.
Mexico: Ok, how much is the fine?
US: Weeeelll... We'll start with your backyard--
Mexico: WHAT?!
US: Not done yet. I like your driveway as well, so I'll take that too.
Mexico: THAT's LIKE HALF MY PROPERTY!
US: Hey, you do the crime, you take your punishment. Not my fault that you assaulted me.
Mexico: ...
US: I do feel a bit guilty leaving you with so little though, so I'll pay for the property.
Mexico: Well, I guess that's ok...
*US takes out pocket change, throws it on the ground*
US: That should cover it.
Mexico: ...