Hi. My mom used a scooter on Anthem of the Seas from Special Needs at Sea. Very easy process - scooter was in her cabin when she arrived and she left it there when she disembarked. She did not have an accessible cabin, so it was a very tight fit for the scooter, but it worked.
My mom thankfully did not have any problem taking the scooter into ports (Labadee, San Juan, Bermuda). But this was on Anthem not Allure. There was a slight incline/decline on the gangway, but the scooter did not have a problem at all (though my mom is pretty small). Be aware that on the return to the ship from port, though, you will likely want to walk through the metal detector separate from the scooter. My mom is pretty mobile and only needed the scooter for long distances, so it wasn't a problem, but I've read on other posts it can be a hassle if you can't walk through the metal detectors to reboard the ship and sometimes have to wait a long time for someone to hand-scan you. But it sounds like your brother-in-law's wife is in a similiar situation (trouble walking long distances), so it shouldn't be a problem. As previously noted, no scooters for tender ports, but you don't have to worry about that because I'm pretty sure Allure has no tender ports (too many guests).
Also, on the Anthem, I "reserved" a space for the scooter on a port day that my mom did not want to use the scooter by telling guest services. Specifically, in St. Maarten, we had a bus tour, so she was able to leave the scooter on level 2, walk off, hop on a cart to the parking lot ($5) and she was all set. I think most major ports have carts/transportaion to get you from the ship to the main area where tours start. But again, let guest services know before hand - they have only limited space for scooters to "park." Not sure if it's the same deal on the Allure, though.
Overall, most of the ship was accessible and accomodating. Scooters are certainly not unusual, and sometimes quite numerous, so RC is pretty good with handling guests with special needs, regardless of which ship.
I'm sure you all will have a great time!