Unfortunately you are still feeling resentful about your last job. I doubt you can really compare both jobs so don't keep thinking about the pay cut (though obviously you can't help that with budgeting etc). Look on this as a stop gap whilst you look for other jobs.
When you are with the children don't think of jobs or money but concentrate on them. As the others have said the child may be doing stuff for attention. He may feel jealous of the other child, perhaps the other one is more favoured by parents, perhaps he would actually like to see more of his parents? It sounds like this is ongoing as there have been a number of other nannies. Praise him and give a cuddle when he behaves, does things properly. It is all very well people going on about Supernanny but you only see the good results, I am sure she had her failures too! Plus she worked with the parents.
Start job hunting now and when you leave, don't see it as a failure. Your next job, whatever it is should pay more or again you will feel worthless (not that nannying is worthless, far from it. I take my hat off to anyone looking after ids, their own or others). But after your last job, your confidence was knocked (as was mine). It might not seem so now, but this job, although not what you wanted to do, might not look so out of lace on your cv. Negotiating with awkward client/boss/workmate - check!
As for your mum - has she been diagnosed by a doctor? Ask them if she could get a health care evaluation to assess how much care she needs in the home. My mum is pretty much bed bound and gets an allowance for carers. SHe has two carers, four times a day (the maximum allowable). Carers do all sorts of things. As I live with her (for now), I do the meals and drugs and (try to!) encourage her to drink more. They top and tail her, change her pads and pants, empty her catheter etc. I also do the shopping.
Hope that helps.