Justkeepsmiling1 I just had to come and post to say that you sound very cool and calm in a good way!
I think you have kept very calm ad replied to posts in a really polite way.
I hope your partner knows how lucky he is to have such a supportive partner.
All the past and stuff about what happened before you were together is in the past now so I would really concentrate on the future.
I think the whole driving or not driving thing is irrelevant. Cars are very pricey to run, and so are driving lessons, better for him to concentrate on earning a living now. Driving and cars can come later when things are more settled. You've said you are both pretty young so there is plenty of time for that.
Personally, I think people have given some good advice about jobs, although they won't be the most exciting ones, there may well be more out there. I've done bar work, waiting tables, cleaning, market research, admin, chamber maid (worst job I ever did was an au pair!). I've never been out of work for more than a few weeks at a time and it does require tenacity to keep on job hunting, but it is possible in most places (BUT in fairness I do not know where you are and of course different areas of the UK have very different opportunities).
Getting back to your original question in my humble opinion I would not fight this battle (if I were in you or your dp's shoes), even if it is or sems unfair. Personally, I think it sounds reasonable for him to do the travelling and to pay for it but even if it is not fair he has mentioned it and I think you said she was not keen so I am not sure pushing the point or arguing would be beneficial.
If I were in your shoes I would encourage your dp to get the best job he can now, work his study in around the job and look to the future. Care work may not be very glamorous but it is vital, the population is ageing so wherever you are there must be opportunities and these may well look reasonable on a CV in terms of working with people if he is wanting to go into counselling.
Personally, I would also encourage your dp to get some careers advice, if he is under 25 it may be available free from a local careers service, or a college if he is studying with a college.
nationalcareersservice.direct.gov.uk/Pages/Home.aspx
And finally to inspire him I would borrow a copy of 'What colour s your parachute' from the local library.
What Color Is Your Parachute? 2014: A Practical Manual for Job-Hunters and Career-Changers
Good luck. Whatever happens in your relationship with your partner I wish you all the best.