As a self-employed Handyman I can tell you this. Any work that is done, be it professional, part-time, hobby or whatever else, has to answer to two primary criteria. As you asked, it has to be worthwhile in financial terms and more importantly in personal terms. In the long term, charging low rates will demoralize her. Not worth it.
Someone once said; "I have no quarrel with he who charges cheaply, because who better then he knows the value of his services"? Obviously one has to remain reasonable. Then there is an ambush factor in working for yourself. I call it syphoning losses since they are extremely difficult to calculate as noted above here already. In the first place they are extremely difficult to detect anyway. Micro-management will not tell you the losses, you can only do it at the end of a period on a balance sheet. Then you have to calculate a fair price in terms of lessons given and monies received.
The trick is to gain a fair assessment of worth to her without her needing to go into the books, just as a simple gut feel. She needs to really feel good about it to maintain motivation for the future. Otherwise, I did it, it does not work.
The other consideration is that when money changes hands it places a benchmark on the tuition and the relationship. One. It locks her into delivering professional work as she already is one. Two. The students will be locked into giving fair and excellent commitment in being taught.
A simple calculation goes like this;
Use the time span of a month as it is easier to break down available time per week. Also remember that there will perforce be extra hours spent in consultation with parents, this is a syphoning cost, it has be calculated.
Difficult at the start, but keep track of it. One other thing. I do not give discounts of extend favours, but I keep my prices reasonable. [[I was told I am some 25% more expensive than the latest quotes, but I kept on getting work with a high execution to quotation rate.]] Floating prices are impossible to track, manage and justify, people talk to each other, whether you like it or not. Do proper, reasonable calculations and be up front to all about how you work. In contract on paper. It just may be necessary to scale prices from beginner to advanced classes.
$50 seems a fair price, I don't live in the States, but about three/four Big Mac's would compare about right. You are NOT selling time, you ARE selling expertise.
Decide how much she wants out of it per month. Forget retirement, you live now. This income will also cover other "invisible" extraneous work.
Determine how much time will be spent in giving lessons. You can only charge for "visible" work done.
Basic Hourly Rate = Monthly Income / Lesson Hours.
Then there's a catch. Research has shown that owners of one man and small businesses spend about 55% of their time in getting new business. So,now.
Charged Hourly Rate = Basic Hourly Rate DIVIDED by 45%.
This could frighten you, but these are hard commercial facts. Things could appear to be extremely expensive. You will; however; have a solid base from which to decide as you go further. The accounting is a good place to start, but she, you both rather, have to feel good about the rewards and the counter performances.
Great success to you both!