I think it would be difficult to fit an
ECV into the back of a van without disassembling it. Taken apart, an ECV has a number of pieces that are going to usually weigh less than 45 pounds. Some are a bit large, but nothing would be too large to lift.
If you don't take it apart, the ECV weighs closer to 150-200 pounds. Since it's not meant to be lifted, it would be more clumsy to lift, with few good places to hold on. Also, the weight is not distributed in a way that it would be evenly heavy - the back will be heavier than the front.
You can usually fold down the back of the seat and may be able to telescope the front tiller enough to make the ECV short enough to fit into the back of the van.
These pictures from Walker Medical show a taken apart ECV in the back of a van - note that it looks like the very back seat of the van was removed to make room for the ECV to fit back there. They also have a video showing how to take apart and stow their ECV. I know that's not what you want to do, but seeing the video/pictures may give you some ideas about how to stow it without taking it apart or may help you see that taking it apart may be less trouble than you thought.
There are in website links and phone numbers for the most often used ECV/wheelchair rental companies in post #2 of the disABILITIES FAQs thread (follow the link in my signature if you don't see the thread near the top of this board). I'd suggest calling some of the companies to ask your questions about ECV and vans. They would know their products best.
As for a handicapped room in an off-site hotel -
it would be good to talk to them and see what that means as far as that hotel. It can mean anything from the entry door to the room is wide enough for a wheelchair/ECV to drive through to the bathroom having a roll in shower and grab bars.
If your FIL doesn't need a roll in shower, ask what kind of shower arrangements the hotel has -
is it a tub with grab bars?
do they have shower chairs/benches available?
handheld showerhead?
if it's a regular shower (not tub+shower) how big a lip do you have to step over?
Many people assume you need a handicapped room if you have an ECV, but depending on the person's needs, you may or may not need one. In most hotels, the room itself will be the same (including the door to enter the room). Usually the difference in a handicapped room vs a 'regular' room is how the space is arranged and the addition of some features.