I am trying to find mobility scooter hire in Dortmund in Germany, do you know of any?
Yes, that's possible. I found at least one company that is renting mobility scooters.
On their website (only in German) you can find the pricelist (under Elektromobil / Scooter 6km/h). You can pick it up, but they also offer a delivery.
This kind of medical stores are called in German Sanitätshaus You can search for it and probably find other stores in Dortmund that are renting scooters.