That's a pretty tall order. While I have had some experience on the south rim, most has been on the North.
1. Indian reservations. My experience has only been with the Navajo. Our information has been that they have adopted the rules and regulations of the state in which the reservation exists. So, for example, if you have a valid CCW for New Mexico and carry your concealed weapon on the reservation, you should be OK. The only reason I am saying "should" is that you are wise to check with the Reservations your are planning on visiting to see if they have any rules that would affect you. I know that Arizona allows concealed carry for residents but I have not researched the law enough to know if this applies to non residents as well. Steve may be able to set you straight here. Check out this website, CCW By State, for more info: http://www.ccwbystate.com/
2. Northern Arizona just got a heap of snow recently and you may want to see what the conditions are like before you hit the road. There are so many places to stay on the South rim that you may want to consider a travel agent (the Auto Club is a great resource) or some internet research. If cost is a factor, there are plenty of places where you can stay that are outside the park that will probably be a bit cheaper. The town of Williams comes to mind - 50 miles south of the Grand Canyon Village, in a very nice area, and reasonable lodging rates. If you are splurging for accommodations, I doubt that you can beat the El Tovar Hotel on the South Rim. See: http://www.grandcanyonlodges.com/el-tovar-409.html
. Great lodging,food, and accommodations.
3. Things to see. Wow, that is the toughest question of all as there are so many. If snow is on the ground, especially in the canyon, you are going to want to spend some quality time catching the spectacular scenery with your camera. With small children, you will be somewhat limited in your activities, but here's my shot:
- The Grand Canyon Railroad, see:http://www.thetrain.com/
- The Grand Canyon Visitors Center
- Hoover Dam - see: http://www.usbr.gov/lc/hooverdam/service/
- Monument Valley
- Sunset Crater National Monument
Good luck, Eric!