I'm a full-time teacher and my son(10) has autism, ADHD and some other problems. He does attend mainstream but has full-time support and can't ever be left unsupervised as he is impulsive, aggressive and runs. He cannot attend any traditional after-school clubs.
I pay a family member to pick him up from school and take him to our house after school; she is £10/hour and it has been ideal. Nearly 7 years down the line, I am glad that I did it, although I did have some reservations about 'employing' family. On some days, I use his direct payments to pay some of his school TAs to take him to clubs after school. I am usually home by 4.30, so it's not many hours that I need to pay for.
Obviously, in the holidays, I am off work with him.
It has been tricky over the years to attend appointments but my boss is very understanding and knows that it's essential; most employers recognise that, legally, parents/carers of disabled children are entitled to time off for things like this. If they don't, they should! In comparison to workers who take the piss with hangovers or have their own dentist appointments/ medical appointments, does it really sound so terrible to a boss for you to have to take your child to an appointment? Every time my son has had an OT/ SALT/ CAMHS appointment in school time, I have gone and asked for the time off, apologised and she doesn't event say anything about making up for the lost time because she knows I work a hell of a lot longer than my contracted hours anyway. The problem for being off in my job is that someone has to cover your class, so you can't really literally make the time back, but I guess in other jobs, you could do that.
I know that I am very lucky with my boss. I am also very lucky that I love my job and I feel much less of a failure in that job than I do in the job of being a parent 
. I wish that my job had less work in the evenings, but I just get it done once my son's in bed.
Having said all this, I started work before my son was diagnosed and before I recognised the extent of his problems. He was a very very difficult child at school in Reception up till about Y4 - very violent and hyperactive, although he is maturing now and is a little superstar in so many ways - and I'm not sure I would have taken on working if I'd known how much extra appointments/ paperwork/ battles were going to accompany his life iyswim. Because I was already working, it probably made it easier to carry on doing it, if that makes sense.