When in Rome, do as Romans do. Hmong people have a saying just like that too bad I can't write in Hmong for my life.
Ruam tiag tiag,
. But fyi, the Hmong saying is not quite as exact as that of the Roman's - in translation and meaning. As a matter of fact, I am guessing you are implying the Hmong verbage, "Ib rab teb ib yam txuj". Thus a more insightful person might argue it is the opposite of the Roman verbage.
You have to have an elder go and talk to one of her elders and express your interest in her, then they'll let the parents know and set up a date for you to go and ua noj. That's about as much as I know.
Ironically, you are precisely "correct" in your observation/comment.
Basically, if one is marrying a "single lady" for the first time then it is the full traditional wedding unless there are circumstances which will vary case by case.
As for a widow, with or without children, but typically this applies more to those with children - the only thing that needs to be done is a dinner (feast=ua noj haus) for the in-laws, letting them know you two are married. Sometimes there are and are not a "bride price" involved - depending on the in-laws, or parents of the widowed lady - in other words, greed versus non-greedy iho. (A widow without children can be considered a "single lady" depending on the circumstances which will vary case by case.)