Depends on the reason for needing the invalid badge I would have thought. It might be well worth considering what grounds to apply on I suspect its very difficult to retract anything that is said in the application and if your GP is signing it they would have to take it into account in considering the HGV renewal.
First of all it’s not an invalid badge, it’s a blue badge. There are several funsters whom I’m aware of, who are wheelchair bound, and one of them definitely drives a hand controlled HGV RV and tows a trailer with his car on. Perhaps they may be along to clarify.