The cart may be the answer for you, but when I used a kids wagon for a short time, it didn't work all that good for me.
I use tote trays like this one.
I have several and each is loaded with products for a specific project.
One has just washing/cleaning products such as:
The body wash. That includes car wash and S&W since I may use either one.
An APC. Happens to be Meguiar's and I use it for carpet as well.
Upholstery cleaner
A window cleaner.
Poorboy's Bold & Bright for the tires
Natural Look for the vinyl
Four Star Ultimate Leather Cleaner
Four Star Ultimate Leather Conditioner
A QD for the water drips after drying. :wall
An AIO such as PwS if I need to touch up an area I notice when washing.
Another contains the products I would use when doing some polishing and waxing. Polishes, paint cleaners, waxes, sealants.
My PC and some pads are kept in a 20" plastic tool box so when I am polishing, I do have to carry both the tote and the tool box to the vehicle.
The cart may be the answer for you, but I would hate to see you spend that kind of money on something that may not do the job for you.