Forget it... I once helped a friend do a similar procedure (taking the engine and manual trans out of a wrecked Volvo P1800 and installing it in another, after removing the engine and automatic trans from that one), and even with proper tools, a lift, and more experience (none of which we had, LOL), it's a big job, and the labor bill would be scary. I was glad we didn't have separate either engine from its transmission, also... and we got lucky that one of the two drive shafts actually fit in the new installation.
And those were mid-70s cars... plenty of room and less wiring, etc. Working in the engine bay or underneath almost any car built after 1980 is like trying to build a brick BBQ pit inside a walnut shell. And if it's front-wheel drive, fageddabouddit!

I don't get your mom's reasoning. Better fuel mileage, cheaper to maintain... and usually a lot more durable.
The only snag with some manuals is that while learning to shift properly, you might wear out the clutch. But it's not hard to learn to do it right, and a good clutch and transmission will take some abuse.
And yeah, it's more fun. More control; personally I think it enhances safety in many situations. I don't mind working a stick in stop'n'go traffic, either, even though my car's drivetrain is trucklike, and the left foot gets a good workout.
Tell her about the safety, the mileage, and the savings... and whatever you do, don't mention anything about hooning.