I'm with the posters who say Mom pays for the carpet/pad, tenents for the subfloor (if needed) and closet carpet.
Sounds like your mom has been lucky to have people who have paid on time and overall have been good tenants... not everyone can claim this.
Yes the cat peed on the floor and it is YUCK - but it happens even to good owners with good pets. Pets get sick, old, jealous, etc.
They paid a pet deposit and your Mom allowed them to live there. Reasonably, she rented to them knowing that she is taking a calculated risk when she allows renters with pets to live on the premises and that there is potentially chance of "pet normal" wear and tear. She still felt it was a good enough business decision with pets to enter into the agreement - so in a weird way she agreed to the responsiblity of what could possibly happen.
The fact they owners didn't request to have the carpet changed prior to moving in, and are willingly paying for the other carpet shows me good faith on their part.
Where your Mom had budgeted prior to their moving in the cost of the carpet replacement, it's not like she is 'out' money to do that part a year later... in fact with the interest that money would have potentially earned BECAUSE of the renters - even with replacement - she is ahead.
AND assuming she had good renters all year (assuming because you are still friends with them and believe their intentions) - I don't see a real question here why what has not been suggested would be a kind and fair solution.
I don't think they should get their pet deposit back - but there regular deposit of over $1000 should be returned minus the fair cost of the closet carpet and possible subfloor.
All the best!