1. It should be.

2. Take I-45 up to DFW, get through/around somehow, and take US-287 to Amarillo. Take I-40. At Flagstaff, take US-89 north to Alt-89 to the north rim.

3a. Take Alt-89 to Kanab, take US-89 to UT-9 and go through Zion NP, pick up I-15 to Las Vegas. A possibility - but I have never taken it and have no info about it - my map shows AZ-389 off of Alt-89 at Fredonia, this goes through Colorado City and turns into UT-59 and joins UT-9 west of Zion.

3b. Retrace your steps to Flagstaff and take I-17 to Phoenix. If you do this, your sister can take I-10 all the way back to Houston.

I am not aware of any public transportation that goes anywhere near the north rim, buses or otherwise.