Hello, and WELCOME!!
I can't help you much with suggestions about renting an RV since we've never rented one, but I'm sure someone here will help. A little more information might help. Are you planning on flying into the States (like into California) then picking up a rental RV? What time of year are you planning your visit since weather is an important consideration when visiting either Yosemite and/or the Grand Canyon? With the size family you have, ya might want to consider renting a larger RV but there's quite a bit of stuff to know about operating a larger rig and I'm not so sure that for a two week vacation it would be a good idea....ya might spend most of your time figuring out, not only how to handle it driving, but also how to dump sewage, fill and/or attach water lines, electrical lines, use slide outs, keep batteries charged, use heaters, and a big variety of other details.....heck, some of us who have been full timing in RV's for a few years already, STILL haven't figured everything out!!! It's NOT impossible, but for a two week vacation, and considering the size rig ya might need, it might not be the best idea. Hope someone else has suggestions.
Steve & Lynette
2014 Newmar 3103 BAYSTAR/Triton V10 w. Banks/05 Honda Element toad