Full coverage on my pickup is only $700 per year. It covers my gator while hauling it.
Get that in writing from your agent. I've been in the insurance business for almost 20 years and have never seen an auto policy that covered physical damage to another motorized vehicle (or trailer for that matter) that is being towed or hauled. Liability for towed trailers, yes, but physical damage, no.
I'm not claiming to have seen every policy written, and you could very well be correct, but I've never seen it.