Badger may not be closed in late March, there's a heckuva lot of snow on the valley floor right now, and I remember them being open for late March visits. Not something to rely on though.
The cabin may be quiet (good choice, not a tent cabin), but Curry will be swamped with kids out on spring break, though probably mostly in big groups with adult supervision.
The 6-mile loop past Mirror Lake to Snow Creek Trail isn't bad for toddler/pregnant wife, and if your wife is a regular hiker you could probably still do the Nevada Falls hike...it will be just the John Muir trail up to Vernal fall, then the Mist trail to Nevada and back, and it's not easy, so use your own judgment, depending on how you can haul the toddler uphill, and how her 4-5 months effects her.
You could go up to Columbia Rock on the Upper Falls trail, though it's a strenuous uphill trail...shady though, and only a mile or so up.
The four mile trail up toward Glacier will be open partway, and it's a nice hike even though you can't go all the way up (steady uphill though). My son carried his 2 year old to the top in a backpack, so it can be done.
Much of the higher country is still closed at that time, but there's still plenty to do and see...the waterfalls should be tremendous.
Gary
Yosemite Photo Galleries: http://www.pbase.com/roberthouse/yo