Hello and welcome to the RTA forums !
With 2 weeks you have the time to visit those places on your 'wish list' but if it's an option it might be one of those trips where a complete loop might work better and start and finish in the same City, whether it be Vegas, LA or SF. Starting in LA it would look something like this; LA > Joshua tree NP > Grand canyon > Vegas >Yosemite [via Death valley and Tioga pass?] > San Fran and down the coast back to LA.
Get the kids interested in the planning stages and let them make some choices along the way and everyone should be happy.
You can use sites like Expedia and Tripadvisor to get a feel of lodging types and costs and what is best suited to your budget and requirements. Most Hotels are geared towards 4 guests to a room which is awkward for a family of 5 but I understand that some are willing to put a fold away bed in a room for an extra small fee, so you might have to do some calling around.
The National park lodgings are generally costlier than that of the surrounding towns but in the summer Months do get booked up early.