There’s nothing we can say here, this is down to Motabilities discretion.
I will say though that, if they lay out the rules strictly and have a tracker fitted, you can’t even use the car for shopping yourself (you don’t live at her address, so she wouldn’t benefit from you going shopping on tuesday for yourself). The car is only to be used for the claimants benefit. If i understand correctly you’re driving 30 miles a week when you’re not caring, those 30 miles you still would need to use other means of transportation if you strictly apply the rules.
What you do in the end is obviously up to you, the issue here is the tracker. If they see you drive around 30 miles away from the person you care for, issues might arise. I don’t know how strict they are with that, but they specify that very clearly in the rules for a Motability car, so at the very least they’d have ground to terminate the lease when they find out.
You also can’t object to a tracker being fitted, if they decide that it’s a necessity. The choice there would be either to get a car with tracker, or no car.
Keynote is simply, that the car needs to be used only for the claimants benefit. If you can, in all honesty and without mental gymnastics say that that’s the case, call them and get the ball rolling. If you know that there’s journeys that would only benefit you (from monday to thursday evening, basically), well.. You have to decide whether or not the gamble is worth it – at least if they decide to fit a tracker, which btw isn’t necessarily mandatory according to their language in the description (MAY decide that a tracker is needed).
If they decide a tracker isn’t needed, well.. Where there’s no plaintiff, there’s no judge. If that makes sense.