Driving in the rain is an all winter event for us and most of this past spring. Our daily commute includes grades of up to 7% on a mountain highway.
Lots of good tips already offered.
One that has not been mentioned is the wall of water that can hit you when a trucker or other large vehicle passes. You cannot see through it for the moment or two it will take your wipers to clear it. Hold your course (assuming the road is not curving and take the pressure off the gas to allow you to slow down a bit.
Also drive with all your lights on. Daytime running lights do not light up our tail lights. In foggy conditions (often accompanies rain in the mountains), being visible to the cars behind you is important.
Hydroplaning has not been an issue for us on the hills, but on the flats where the road is not properly canted or where a dip has formed it can be interesting. We treat it the same way we do black ice (often forms in the same places), take foot off the accelerator and steer into the slide.
As others have said the first rain after a long dry spell makes for slippery driving, but soon the road grime washes away and you are left with just the water to contend with.
I hope it doesn't rain on our trip back from Oregon to Socal along Hwy 101, lotsa grades and snaky 35mph curves, narrow sections, road repairs to kept me occupied on the way up the coast. Camping in the redwoods, etc. is wonderful.
Those yellow speed signs they put on corners were made for vehicles like us. You may need to take a bit off that for rain. Where I live if you stopped to wait out rain you'd never get anywhere. Good tires help but the up side is RVs don't hydroplane as easy as cars as the tire loading per square inch is much higher than a passenger car. The tread on RV tires is generally much more open too so they pump water really well. I don't worry about changing any of my tires until I am about twice the depth of the wear bars on the cars. This can vary as the rain hits here in mid October for the big wet until about June. If I am going to need tires over the winter at all I just get them before fall. The RV will likely time out on tires before they wear out but I'd likely want a bit more tread for winter driving on it (snow). No way would I freak out and demand new rubber on it all the time. We carry a windshield washing squeegee and use it when we stop for fuel. One person pump and one washes glass. Make sure your washer fluid is full. Rain X is good stuff if you wish to take the time to apply it. I use it on my cars but not the RV as it's a pain to put on it. My surge protector gets wet if it rains. If you look at mine it is designed to have one end up in rain. I have to ford water of more then a few inches frequently. I live in a flood zone. If you are going to ford water, walk it first. If you can't walk it or it is too scary to walk you shouldn't drive it. If you don't know where the road is, go back. If the road is closed, it is for a reason. I will only take a vehicle (off road vehicle or tractor) out in a really seriously flooded road if I know the road really well and will take it easy. I only do it in an emergency...like if out of beer. The odds of doing it in a RV are slim to none. If you ever do give your wheels a good dunking be sure to drag your brakes a bit with your left foot to warm them up and get the water out. Then you won't be suddenly surprised with ineffective brakes if you need them. One really nice thing about an RV in rain is you are up higher than a lot of the spray and headlight glare on the highway. It is much less stressful than in my hot hatch looking up at semi tires. I would only quit if it's a massive gully washer and visibility becomes an issue or the anti destination league is trying to kill me....usually backing down is adequate. If you are not comfortable you can pull over and take nap feeling very cozy in your mobile shelter...or listen to the rain and read a book.