Regarding a mattress cover or shower curtain vs puppy/nursing home pads: Do you REALLY want to deal with washing a matress cover or shower curtain (shower curtain is gonna have urine sliding off anyway potentially onto the floor), much less during your trip? The answer is no, you absolutely don't. I lived with an incontinent dog for two years (well she was a decade old dog but only during her last years became incontent in her sleep) to where it was cleaning her kennel at least half of the week, and believe, it is MUCH easier and less gross to just fold up the puppy pads from the corners (or even put them in a plastic bag for the trip to the garbage), bolt to the trash can and throw them away than it is to have to deal with this pee soaked thing you have to wash. The more liberal you are with your use of puppy pads, the less chance there's gonna be any soaking into the hotel room. Puppy pads are also cheap.
Also:
1. Consider double layering the pads. My dog with her tiny bladder sometimes soaked through a layer of them.
2. Buy latex glove for handling soaked pads
3. Try and have your kid go to the bathroom before bed. Less full bladder has a lower chance of going accidently and lowers soak through chance
4. Best case scenerio, you don't ever have to change pads and you prepped anyway.