Without full coverage on your vehicle, it looks like you're going to be doing all the footwork for your accident. But, even though it can be confusing, there are several things you can do:
File an amended police report. Sure, it won't be in the reporting officer's handwriting, but it shows you disagree with his version of the accident as listed on the report.
It's very interesting that you mention that the vehicle to your right managed to pass by smoothly. This would indicate, of course, that you hadn't hydroplaned into the right lane.
It doesn't sound like there are any witnesses to this accident. That's problematic, because the people in your vehicle and the motor home would not technically be considered independent witnesses. Still, if you end up going to court, you'll want to bring along any adults who were in your car.
Consider the point-of-impact when dealing with the insurance carrier of the motor home. If it was a dead-on, rear-end hit, it essentially falls to them to prove that you are liable for this loss. This is very, very difficult to do, so that's in your favor. Really, the insurance adjuster would need a witness beyond the other driver to prove you came into the motor home's lane so fast that the motor home was unable to stop.
But ... will that matter? It depends. The other carrier may still deny liability, relying on the police report and their driver's statement. They may even go after your liability coverage to pay for damages to the motor home (you'll want to stay in contact with your carrier to get updates on how they're handling the claim). Also, if the other carrier knows you don't carry full coverage, they don't have to worry about your insurance coming after them or arbitrating the claim. They may gamble that you won't pursue the claim as far as court.
Since you don't have full coverage on your vehicle, and no payments will be made by your insurance carrier, your final option is take the motor home driver to court (assuming his carrier doesn't pay for your damages). There are several strategies to consider when taking someone to court over an auto accident. If neither you or your passengers were injured, you don't necessarily need an attorney. If you were, it might be best to contact one. Some things to consider about going to court:
a. Decide if small claims or civil court is best for your case (your state or county statutes may not give you a choice, so take a trip to the courthouse to do some research).
b. In small claims, attorneys aren't allowed. This may mean that even though you're suing the other driver, his carrier may not be prompted into settling with you because they don't have to worry about the expense of providing an attorney. Instead, just you and the other driver have to show up, though the other driver's carrier may send a representative to guide their driver through the proceedings.
c. In a civil case, you'd both want an attorney. This usually prompts insurance carriers to settle, because they will typically make a business decision (ie, how much do we want to spend?) regardless of liability.
d. Mitigate your damages! I cannot stress this enough. If you're forced to take the other driver to court, you can expect long delays and months before you actually stand before a judge. If you expect to be compensated for, say, loss-of-use (ie, rental) during that time, you'll be sorely disappointed. All "mitigate your damages" means is that you do what you can to lessen any damages, and that includes expenses. It would probably be best, for instance, to go ahead and replace your car if it's a total loss.
A good attitude to keep during this whole thing is that the other driver's insurance company doesn't "owe" you anything. Their contract/policy is with their driver, and they will act accordingly to protect their driver. This may sound harsh, but your carrier should do the same for you. It'll also keep the whole process less frustrating for you (believe me).