Two hints
1) Nemo - if you think anyone might be claustrophobic, there is no wait in any line to ask to use the disability version of the ride. It's a little room where they show a filmed version of the experience. All you do is go up to the CM at the juncture of the sub line and the monorail entrance ramp and ask to do that version. Sometimes my little one just doesn't have the patience for the sub unloading, so we have been told it's a good option for us, if we didn't want to do the line.
2) TSMM - the single rider line is a good option. If your kids are old enough or if you are "child swapping" and don't want to go on with the kids, this option is definitely good. We used it last time we went to DCA and it worked great. My husband took the girls on King Triton's Carousel and I rode, then I took the kids while he went. The Single Rider line was super short.
If you have older kids and you have 2 adults, have 1 adult go, sandwich the kids, so they can go next, and follow it up with adult #2. That way one person is waiting for them to get off and one makes sure the kids got on okay. The ride isn't very long, so if there is only one adult, then decide whether you want to wait for them have them wait for you. The person waiting can stand at the foot of the stairs, so they can easily be seen by everyone involved. I would put it high on the scale of a very safe place for an older kid to wait for an adult. Very limited traffic access - only from the 16 people leaving the vehicles at a time, and a ton of CMs there, keeping an eye out.