According to the PHB's rules: An animal pulling a carriage, cart, chariot, sled, or wagon can move weight up to five times its base carrying capacity, including the weight of the vehicle. If multiple animals pull the same vehicle, they can add their carrying capacity together.
As defined by PHB Base Carry capacity is 15xSTR = 270lbs
Per vanilla rules Cat could pull: 15x18=270x5=1350 lbs.
This is the number we will use and I am no longer negotiating this. The cart weighs 200lbs, Cat will put on the collar like a mule and pull comfortably, the collar and harness is 40lbs, this will not subtract from her tow capacity directly, the cart is 200lbs, the spare parts 50lbs, and other non-removable items like mule feed is 10lbs per day which is 100lbs for 10 days that will feed two animals for 5 days without access to rough forage.
So given the Cart can handle 2000lbs, if pulled by a mule 5x420=2100 a single mule could pull nearly the fully loaded cart. Of which the net load would be 2100-200 (weight of cart) - 350 (other carried items)=1550lbs net.
With Cat pulling the cart, 1350-200-350=800lbs net in addition to what she is carrying on her person, so don't worry about subtracting that.
This is reasonable.
Also keep in mind that the tow capacity is not a constant load, on a straight and level road the actual load is a fraction of the total, the full load Cat or a mule would be capable of pulling would be when the cart is being pulled up a rutted hill at full speed.
So in conclusion, the capacity of the cart is 1550lbs net if pulled by a mule, and 800 if pulled by cat.
Additionally, each mule that is not pulling can carry 400lbs net minus their packs and other accessories. So if a mule is pulling, the total capacity is 1550+400=2050lbs, if Cat is pulling it is 800+400+400=1600lbs.
Make a section on the inventory sheet for what is in the cart + Mule packs out of a total of 2050lbs knowing that if the amount is over 1600, a mule must be pulling.