i realize why motability do what they do, but i think there should be a bit of common sense on their part you are helping your mum at least 35 hours probably more , you are going to uni to better yourself to allow you to get a better job which effectively benefits you but most importantly will benefit your mum. i feel motablity should look at your case again with the understanding that this is to benefit your mum. if they don’t budge on that then there are a few other options you can try.
I understand you get a bursary and student loan , you advise the uni guidance teacher you are full time carer tell them about motability problem, ask them for a discretionary funding as a carer for a taxi to and from your mums and uni , you can also get a free laptop from them as well also there are other things they can help with you get extra time to submit your work.
there’s a website called Turn 2 Us that you can check what benefits you and your mum can get, there’s a section about grants and there will be lots of help there for you just put in your situation and you can apply for grants …
i hope this helps