I had Hagerty while I was restoring my Roadrunner. they would not write "MY" agreed value after the car was completed. I changed to Grundy with no problems of my agreed value. It was a little higher premium. Car is covered anywhere it resides, parks, is driven, or trailered by me or others. If it is trailered by a nationwide transportation carrier, then the Carriers insurance would be Primary. Just lost my home to a fire (car was removed before the fire got to it) but homeowners insurance would not have covered it as it was considered an Antique. Hagerty has an ironclad section in the policy to tell you they will not cover it if it was raced. Have not had a claim so I cannot speak to that.
Just my 2 cents.
PT in Tennessee