The higher elevations thru mountain passes are the only intermittent worry that is short lived during April should snow conditions arise for Southern Nevada or Southern California...
March and early April is windy season for the deserts with sometimes nasty duststorms, which can also bring rain once in a while...but other days in between it is perfect weather in the deserts.
I would say the only concern for after the first week of April while in Las Vegas is the daytime temperatures can reach the lower 90's F or lower 30's C while clear...unless these hotter temperatures are bothersome, an umbrella to carry around for shade and-or a redneck air conditioner (water spray bottle) is great to have for a deterrent during the afternoon days which worked for me while outdoors.
Anaheim is pretty much coastal weather that is practically perfect temperature wise.
March travel can be hassle free thru the passes and higher elevations on certain western routes as long as the jet streams behave, then again it's a crapshoot of course.
Although Disneyland is usually a pretty busy place year round, I would try to get that visit over with before late May at the latest because of the Memorial Day Weekend which kicks off summer thru Labor Day Weekend, as many kids are out of school by then and gets even more crowded.
Mid March to mid May would be the timeframe I would be shooting for a trip like this, but weighing the options between putting up with early on potential road condition delays or later on in the desert dealing with blistering heat.
