They are at a tricky age. Back when I was that age, I recall walking home from school and having a key to the house, so I could let myself in. Would then be on my own for a little bit, then my older sisiter (18 months older) would get back from school, and around 1.5 hours after I got home, my mum would get home from work. This was back in the 80's, attitudes to children being left home-alone have changed over the years, so not sure this sort of thing would be accepted these days.
After-School clubs are usually the soluition, but as your 10 year old hates it, you are now stuck. Are there any after-school activities your 10 year old could do? I remember that twice a week at school, after school hours, I did orchestra - and one evening a week I walked to a local leisure centre and did a roller skating course. I was 11 or 12 at the time, as I remember walking from senior school.
A childminder may be able to provide childcare - but at 10 and 12 your children may not want to be around younger children. Could be worth asking around to see if any childminder can help.
Your children's friends parents are another option. Can your children go to someone's house to 'play' after school? Could work for short periods.
Anyone else got any ideas?