I did mean to tar you with any brush there - aseriouslyblondemoment. But of course your situation is not the norm. Most people do have access to childcare and don't live in total rural areas. I am referring to your situation as an example as you have gone into detail, however this is not a personal attack, just my opinions in general put into a relative example.
Of course not many jobs totally accomodate the needs of our children. I would much rather not have to leave my dd with Childminder, but I have to. Our after school club isn't at our school it's at a nearby one, the holiday club is in the next town, so I will have to travel there before going to work during the summer holidays. All inconvenient and a pain in the arse, but many have to do it. Also, I understand you are rural, but surely there are childminders still - they often offer school pick up and drop off.
I am currently on benefits, after redundancy a few months ago, but I'm due to start my job next week. I get no child maintenance so have been coping with I/S, CB and CTC for 3 months. Of course I only have 1 daughter, but more kids equates to more CB etc, so it's all relative. We have done just fine, not luxurious but not living in poverty by any means.
You mention having a car and owning your own house. These are things many single parents, and indeed many working couples cannot manage to have. So I would say you are not doing that badly not working.
Perhaps if you are really in such a rural area then you may need to move to have access to closer amenities, childcare and jobs? I know I could not work if I lived in a rural area, especially as I cannot afford to run a car, and probably won't be able to when I'm working either. Just a suggestion.
I still think that parents who are jointly financially resposible for their children (either living together or living apart and paying maintenance) should not be entitled to benefits such as I/S.