nIvnav vItuQ
I put on the pajamas

vIghro'wIjvaD nIvnav vItuQmoH
I dress my cat with the pajamas

So, the tuQ is used when I put on clothes, and tuQmoH when I dress someone else.

Is my understanding correct ?

I believe it is. You're going to get some people who think otherwise, that tuQmoH means something other than what tuQ + -moH means, because the translations in TKD are confusing.

tuQ wear (clothes)
tuQHa'moH undress
tuQmoH put on (clothes)

I believe tuQ refers to having clothes on rather than putting clothes on. HIpwIj vItuQ can be used to describe me already in my uniform, not the act of me putting my uniform on. If I say HIpwIj vItuQchoH (notice that's -choH, not -moH), it means I go from a state of not having my uniform on to a state of having my uniform on, but it still doesn't say anything about who caused this state to be. That's where -moH comes in.

HIpwIj vItuQ'eghmoH I put on my uniform; I cause myself to wear my uniform
puqwI'vaD HIp vItuQmoH I dress my child in the uniform; I cause my child to wear the uniform
HIpwIj vItuQHa''eghmoH I take off my uniform; I cause myself to un-wear my uniform
puqwI'vaD HIp vItuQHa'moH I take my child's uniform off of him/her; I cause my child to un-wear the uniform

Notice that tuQHa' is not separately defined in TKD. Un-wear is not something that someone would look up in English, so it does not appear.

You could say something like HIp vItuQmoH, but this would mean you put someone unspecified into a uniform, in the same way that Hol vIghojmoH means you teach someone unspecified the language. But it doesn't mean I put on the uniform, which means specifically that I am both the wearer and the putter-on. HIp vItuQmoH means only that I am the putter-on; the wearer is unspecified.

-- 
SuStel
http://trimboli.name