Here's the thing, if cell phone coverage is the basis of where you are going to go on this trip, then you are practically limited to using only interstate highways. As you get into the rural areas of the west, cell coverage is going to become very spotty.
Of course, people were taking roadtrips for decades before there was even such a thing as a cell phone. If you break down, you'd have to wait for help. Of course, before any trip you should also be making sure your car is in top condition before you leave, by taking it to a trusted mechanic. You should also know how to do basic things, like changing a tire, because even with a cell signal it could take a few hours for a tow truck to reach you in more remote parts of the west.
Tioga Pass, along with several other sierra passes are not plowed in the winter - which closes them typically from Nov-May or so, if you are leaving anytime soon, this should not be an issue at all.Google Maps says the road cutting across Yosemite "may be closed seasonally". Will this road be open and in safe driving condition this time of the year?