You did not say who you are currently insured with, but I'm insured with AllState and been very pleased with them. Of course, we have everything insured through them ... house, auto's, trailer, even life insurance. We used them for rental insurance in our younger days. AllState may not be the cheapest, but they are definitely trouble free when making a claim.
We had one situation when my teen-age son was involved in an accident and the other guy's insurance lawyers started threatening law suits and such directly at us. AllState's lawyers jumped in and proved the other guy was committing fraud, (proved it), and the other insurance ended up paying everything. We never set foot inside a court room. AllState lawyers took completely over when we received that threatening letter. Sweet.
For such service as this, we've been loyal to AllState ever since.
One thing you need to consider if you break ranks from your house insurance company:
Our homeowners policy covers us while we are camping. In other words, it covers all the contents of our camper (personal property), including computer theft. Also, while camping ... slip and fall is covered under our home owners policy, as well as dog bites and such.
As explained to us, if we took the camper and shook it upside down, everything that falls out is covered under our homeowners .... NOT the trailer insurance.
Trailer insurance covers damage to the trailer when not in tow, including theft.
When in tow, any damage is covered under the automobile policy.
So you really need to make sure if you break the "bundle", you are truly covered for every possibility.