As someone who suffers arthritic problems, I would consider taking the elevator down rather than attempting the long downhill walk from the natural entrance. There is plenty to see in the Big Room section accessed by the elevator, but there is really nothing to compare the feeling one gets walking in. As for the bat flight, it may be asking a bit much to stick around until dusk after tiring out walking the cave so the idea of doing the bat flight the night before might be the better alternative. I suspect the bats do not put on the same show (density) that they do in mid-summer, so researching that would be worthwhile before deciding.
Sitting Bull Falls is not that predictable since the amount of water depends on the recent rain/snow falls. At it's most vigorous, it's not that large of a volume. As for swimming, again the volume of water does form pools both above and below the falls, but more suited to soaking and cooling off in warm weather than actually doing much swimming - relatively shallow pools in both instances. It's a long way from anywhere to the falls, and should be considered an all day trip. The narrow road is paved all the way.
White Sands can be a half-day experience, depending on personal interests in rolling/sliding down the dunes. In April, with an early dusk, that would be a great time to visit if photo ops are important. Sunsets are almost always magical. And if possible to schedule on one of the "Full Moon" nights-that is truly a magical experience.