Yobiks,
I will take the opportunity to answer your Depends question as an experienced user and DaVinci lab rat.
(My surgeon had not done the 'requisite number' of surgeries, and I didn't know there was one until long after surgery. I visited here the first time a couple of months after my surgery, and got some of the same feedback. I try to ignore that, because the vast majority of HW wants to help you.)
Back to the trip home.
I got a pair of loose exercise pants, and cut the seam at the knee so I could put the big catheter bag (empty and folded) through the hole. A pair of 'basketball pants' (snapped down the side) would accomplish the same thing.
I suffered bladder spasms constantly, and leaked badly around the catheter tube, so on the way home realized it was to be a very wet trip. I stopped at a pharmacy and went in, bag and all, and bought some "adjustable" depends. Those open on the sides with a velcro-like tape, so you can just strap one on without undressing completely. Glad there were no kids or police around.
When I went in the store I had the bag in a shopping bag - the girl at the door wanted to check the bag - my first exercise at really dark PCa humor - you can imagine how that went.
I used those when I went out with the catheter. In the car, you may want to get some 'underpads' - adsorbent disposable pads, to put in the car seat, chairs at home, and under the bedsheet.
I switched to the normal Depend pants once the catheter was out, with a booster guard (Walgreens mens guard is the most absorbent I found). To keep the cost down, I used a Walgreens womens overnight pad at night, but they were much too bulky for daytime use. That did keep me down to doing the sheets a few times a week instead of every morning.
If I didn't have a major flood during the day, I just used the same pant overnight.
Eventually I got to the Depends pant with Depend guard, then regular jockey shorts with Depend guard.
As to sleeping with the catheter, it was problematic. You can't crimp the tube, and the big bag has to be lower than your bladder at all times. Don't try to sleep with a leg bag. I had a big (14 liter) squatty bucket - put that on the floor, hung the cath bag inside. That way the valve stays upright, and if the drain clip comes loose (it likely will once or twice) at least you've peed the bucket instead of the floor.
I got several cheap pillows and used them to block my sides so I would not roll over on the tube.
The system worked well, and with the minimum of pain meds I slept through the night without major incidents.
All of this from my happily fading memory of life with Cath.
If I haven't already, let me offer another Welcome, and a wish for a good outcome. Sorry your first posting was rocky.
(edited typo)