well, if she is jobseeking, she's entitled to the jobseekers allowance. if she's not jobseeking, then she doesn't qualify and needs to work out what other benefits she might be entitled to. (as she feels unable to work, and i assume is content to remain in receipt of benefits)
maybe she could look at before and after school care so that she could work? (many people do this, with children with diagnosed disabilities) it depends whether she actually wants to work tbh. she doesn't sound keen.
dyspraxia is of course one of those things that does affect children differently, but at 13, if he is not receiving much in the way of additional support (and has managed so far without) i really don't think 'i have to take him/ bring him home from school' is going to fly.
her local job centre will have a 'back to work' advisor, who specialises in helping women return to work after child rearing etc. they are usually very helpful at discussing childcare options etc, i was pleasantly surprised (i have a 7yo with cerebral palsy and a 9yo with medicated adhd - thankfully the 11yo is nt
)
i'm not impressed with the govt (this one or the last) provision (in terms of financial etc) to get parents of children with disabilities into the workplace (damn near impossible unless you qualify for direct payments), but tbh it does not sound as though her son needs specialist care - just someone to remind him what to do and when to do it. wearing, in itself, but not unlike most 13yos. if he does need more specialist care, then she needs to discuss his needs with his ot etc, and sort out a dx, apply for dla and then carers allowance. i don't think it is usual for dla to be given for dyspraxia tbh, but the ot/ physio would know.