How about Ridgeview Apartments? They are in Olathe off of 119th & Ridgeview. Also, when you are not working and are at home with your son, have you thought about watching a few kids during the week to get some extra $$? Every little bit helps.
As for finding someone to watch your son 8 hours per week, what about a Parents Day Out Program? I know it costs money, but if you need someone to watch him, then you may be forced to let someone other than family watch him.
Or have you thought about doing daycare full time? Just some options.
What about applying for state assistance for health insurance for your son? Healthwave? I know my cousin has her son on that and has been very helpful having it. She had no insurance on herself, but just recently found a job and was able to get her own health insurance.
Hope this helps you out. Hang in there. It will get better. Just think, all the sacrifices you are going through now, you will be very grateful for as you are able to be with your son.