No. I'm in the same boat as you, since my wife hates driving my truck and has never driven the rig.
Lay out reasonable, logical arguments:
1) She has almost no experience driving your truck.
2) She has no experience driving the rig, backing it, or hitching and unhitching
3) She has no experience driving something that weighs ~20,000 lbs - stopping distances, anticipating, paying attention to height clearances, etc.
4) Would she let a total novice take custody of the two children for the weekend driving a vehicle they are completely unfamiliar with?
If nothing else, as a father, you have to say no, and be firm about it.
Fortunately, my wife is a lot smarter than me, and would never even consider such an arrangement. She knows she's not a very good driver.
Like said below - take one for the team and do the driving yourself.
