Yes, yes, I know. Not for everyone- but I've got a few tricks up my sleeve on this one.
First of all, we have 20 diapers for 2 children. No, that's not much, about a day and a half's supply. I only wash 16 of them at a time- one on each kid, plus a change ready to go for each kid. We don't do cloth when travelling- whether it be for a day trip or an overnighter. It can be done, we just don't do it (to save my sanity).
Diaper laundry is not nearly as daunting as it sounds. I use a wet pail, which basically means that I use a pail that once held kitty litter filled with water for the diapers waiting to be washed. I change the water a couple of times per day- but again, I only have a day or two's supply of diapers.
When it comes time to do the diaper laundry, I drain as much of the stinky water off as I can, then dump the diapers into the washer and run a full cold cycle to get any yuckies off. Then, I pull the inserts out of the diapers, and run the hottest water I can into the washer, adding a "half dose" of laundry detergent (right now I'm using Arm and Hammer free and clear laundry detergent) and then letting it agitate for a couple minutes, then stop the washer for an hour so that the diapers can soak in the water and soap mixture. Then I come back, turn the washer back on, and run the longest hot cycle with a double cold rinse. After that, I run one final cold rinse cycle- and I always double check to make sure there are no suds during this rinse. If there are, then another rinse is on tap. The key is to make sure that there is no soap residue on the diapers!
When the washing is finally done, into the dryer they go. I try (emphasis on try) to stuff the diapers when they're finally dry, but that doesn't always happen. We usually have to purchase about one package of diapers per month for the kids- both are in the same size so that's a big help!
One thing I would do differently if I could do it all again- don't buy velcro, buy a few more diapers, and buy a tub sprayer attachment immediately. The velcro means that everything sticks together, which is kind of a pain. The tub sprayer and extra diapers will be a big help when we finally get them, but that is yet another thing that is on the back burner for now.