Hi, I'm new here and I'm a native Japanese who is learning English.
I happened to read this thread and found it very interesting because I myself wanted to move to the US when I was young.(I'm of your mother's age, I guess.) So, I really feel sympathy for you guys and want to help you with some information.
Hiragana Times
However it doesn't contain info on free Japanese classes, you can find the practical information on Japan at this site.
Sakura House
One of the most popular house agents for foreign people in Japan.
I hope they will be of some help.
Nyororin, I really felt for you reading your hard times with your mother. I'm happy to hear you are happy now. As for your terrible experience through the trip with those English teachers, I think their rude attitudes must have come from the minority's 'ressentiment' in a foreign country. The same was
true in the Japanese tourists' case I met in Hawaii. Everybody seemed to love the island, climate, food and people, but when it came to the conversation, I couldn't help thinking that they were TRYING to complain. That's the reason why I quit joining group tours.