Mishka-- Don't expect ANYthing from him. Then, when something comes along like the lawn mowing, you will be pleasantly surprised. The R between S and stbx must be just that--THEIR relationship, to work out. Snooping will only bring you more pain as you witness things you can't control. If you wanted him to give S a ride, you should have texted him yourself. Its not only to be easier for you--it is also for him to remain a responsible, involved parent. Keep it very simple and business-like: h, can you take S to TKD today?
Classes-ideas: Check the local library for some. Also, local craft stores often have one-time classes. Home Depot has workshops on do-it-yourself projects (power tools are AWESOME!). Look online; youtube and other sites offer free classes on almost anything. Get some workout dvd's free from the library and do them at home--son may even join in.
Mom-care: Check with the local VNA and Senior Center to see if they have caregiver respite services. It may only be once or twice a month, but let's you get out guilt-free. Set her up with a phone-date with other family and friends, dial it for her and run! Set son up with a tape-recorder and box of old photos to get all of those life-stories down (while you go get a pedicure). Ask the Senior Center if there is a home-bound or other lonely elder in the community who needs a companion--tell her that they need her help, set her up to call that person. If you are members of the church, maybe the clergy would stop over once or twice a month to visit.
Take care of you--you are VERY important to quite a few people, not the least, your son!