I have absolutely no experience in any sort of professional teaching environment (my only teaching experience comes in the form of teaching my classmates), but I can tell you what my current once-a-week 2-hour Japanese class does. I can also tell you a bit about Genki, as it’s the textbook I’ve been using for the last two years.
Things about Genki
Though, before heading to Genki at all, you might want to consider whether or not your mother’s neighbors can read ひらがな/カタカナ. Genki does provide Romaji for the first two lessons along with charts, but it doesn’t really do much in the way of teaching ひらがな/カタカナ, and approaching it without having a grasp on ひらがな is a bit difficult. Tofugu has some things on those that helped me a lot when I first started learning Japanese.
Another good thing to note about the Genki textbook is that they have a website with videos and conjugation practice activities for all of the lessons. That, and if you want to assign homework, they have a workbook that goes with the textbook. A lot of the exercises have corresponding audio clips on the disc that comes with the textbook.
One thing about Genki’s furigana is that it’s really small. Depending on how old your neighbors are and how good their vision is, they might have trouble reading it.
Genki lessons per class
One two-hour Japanese class is usually enough for one or two grammar points, several Genki exercises, and kanji practice. I often find it useful to do an exercise right after learning something. It’s sort of like how you usually get a practice sheet after learning something in math or how a review comes shortly after a lesson in WaniKani. Concepts need to be reinforced to be remembered well. (Probably)
From what I know, we go at a pace of approximately 3 weeks per 1 Genki chapter. Depending on how your students seem to be doing, you might want to take it faster or slower. Also, think about which chapters might take more or less time than others. It might be beneficial to spend more time on something if they have trouble with it, or less time if they find it really easy.
In terms of cutting material, I’m not sure there’s much to cut in Genki. You could cut the vocab, but then the dialogue and exercises won’t make as much sense. You could cut the dialogue, but then you’d miss a chance to introduce/reinforce the grammar within context and have your students practice speaking. You probably wouldn’t cut the grammar. Cutting the practice exercises would shorten things, but it would probably lead to less practice. You could most likely cut the kanji, though. Each lesson has furigana on everything, and Genki might not be the best thing for directly studying kanji.
I’ve run out of time, so I can’t write more, but there’s hopefully some speck of a useful thing in there.