I am not sure I follow the question?
You can't get a tax rebate where there is no tax to rebate.
The position is that it is for your child to either refuse to use their own vehicle and subsidise her employer or to renegotiate the travel expenses OR to accept the situation
To deal with the link
@User quoted, at point one of the guidance it states
1. Overview
You may be able to claim tax relief if you have to use your own money for travel or things that you must buy for your job.
You must have paid tax in the year you spent the money. How much you can claim depends on the rate you pay tax.