You've had good advice re carers allowance / UC above from others that know more about DWP- carers allowance is what the carer claims direct once their carer for person gets AA or PIP and you're right it has strict criteria of who can claim that (including your income and if you do over ?35 hours care to her a week?)
I'm an adult social worker, I can't give you individual advice as haven't assessed but possibly can make comments in general terms of what publicly available info would tell you.
Your mums AA (attendance allowance) is to pay for additional support/ care she needs as a disabled person.
Yes she can pay you using her AA, and her using it to pay for your travel costs to visit to help her is also fine!! Or more than that, she can pay you for helping her! It has to be her choice of how she spends her AA and how much.
It is perfectly appropriate for her to use it to pay you or anyone that is providing her care support. Yes people sometimes pay their relatives using AA- as your list of prompting and reminding her and being available to her (etc) (when she has already been recognised as having a level of care and support needs, as she's entitled to AA) falls under you providing her with care support.
I imagine your mum far prefers paying you or giving you a bit of money towards the help you provide, than paying a formal carer through a care agency or employing a PA (personal assistant)
Do be aware if she formally pays you for care hours, rather than donates towards your costs directly extra to you for helping her, that may be considered an income by HMRC for you. (You'd have to read HMRC /UC info yourself)
For more help with care for your mother, you can discuss with her whether she would agree to you making a referral for her to have a social care assessment (under the Care Act 2014) by her local adult (care) services.
It may be a wait to get that assessment booked in but they can identify many options including telecare (lifeline alarms) and community facilities (lunch clubs, etc) which are useful as can help as preventative services. As well as identufying if she isn't managing with current support and has needs for a care package or funded services, like day care etc. That's financially assessed under LA charging policy , but they may take into account if she is using her AA to pay for care that might have been funded by LA otherwise (eg your support). Do have a look at her county councils adult care website as there will be plenty of info on there.
Also as her main informs carer, if she is assessed as having eligible needs under the care act herself, even if she doesn't have a formal care package, you can ask for a carers assessment in your own right. At this stage that may not get you anything funded for you (ie if you aren't doing 24/7 care in need for funded carer break cover) , but it's a chance to talk about impact on you and be given advice on carer support services such as local peer groups, and for eg local dementia support groups for carers and many other local community support carer initiatives in the area.
Sorry I can't help with children in need (ie child disability) services options as CSD (children services dept) is different to work done in adult care services dept, under different legislation- but there should be info online for that CSD in your LA too.
Hope that is helpful