(I assume you are traveling by car and so have a lot of room to pack gear.)
I remember staying at a hotel when my son was 1-1/2, my husband and I hung out in the bathroom so that my son could have a completely dark room to fall asleep. Can't remember if it worked.
Guest bedroom - we stayed at a friend's for a week. With their permission, I pushed the bed to the corner of the room, and brought along a toddler aerobed (air mattress) and put it on the floor right next to the bed. I put both my 1 y.o. and 3 y.o. on it, and sat on the floor next to them while they fell asleep.
Booster seats - I have a kaboodle (from amazon) which works great if the chair and table are right, but if they are not, then it won't work. I also have the fisher-price travel booster, which comes with the tray that can be used or not. In a pinch a big thick phone book might be enough.
Bathing (assuming bathtub, not shower stall) - I brought along a 5-10 gallon (I'm not sure of quantity) plastic bucket and a non-slip bath mat. Then I used a small container - plastic jar, big gulp cup, whatever - to pour water on the kids, then soaped and rinsed the same way. For the water-sensitive, you might ask her to cover her eyes/face with a wash cloth, but of course it won't be 100%.
When traveling, you have to wing it. Try to keep to a modified routine but know that most likely it won't work. When traveling I disregard bedtimes. I still keep to the bedtime routine - calm atmosphere, telling my kids that it's dark outside, people are going to sleep, etc - but wait till I see definite signs of sleepiness. The trick is the catch the right moment that they will fall asleep when they hit the bed, but not get overtired and start an adrenaline kick.
I also try to arrive during the day. That way I can take the kids on a "tour" of where we are staying, checking out every nook and cranny ("oh look, here's the light switch!" "Here's where we'll be sleeping!") and point out similarities differences to our home.
I don't try to keep afternoon naps. Instead I try to time long drives after lunch, so they will sleep in the car. They might wake up cranky, so I expect a "decompression period" afterwards.
Hope that helps, and good luck!