This answer does not exactly cover your case as what we put in place was for our children and the chores they needed to do. I went though the "me vs. my wife" stage when our children were small so I completely understand your pain (this is to say that you are not alone and that many people go through that)

We first tried the "you are old enough to manage" which was of course a disaster. We then forced them to use a piece of paper but it was never clear who did what.

I ended up writing an app that

• has an interface for each child and an administrative one for us
• the interface is very simple, but we did an important thing as we found out afterward: we added "fractioned chores" where due. Typically loading the dishwasher brings in 0.2, 0.50, 0.75 and 1.0 points. They are surprisingly honest on the fractions.
• the chores are independent, each of them has its own counter
• what constitutes a chore was clearly defined ("cleaning the kitchen means this and that")

The results are available on their app and on the home dashboard

The fun part of that added value, as well as the fact that there is a current count and clear "whose time it is".

This may not be relevant to you as the fun part when having very small children can sometimes be microscopic (but this will improve!)

This answer does not exactly cover your case as what we put in place was for our children and the chores they needed to do. I went though the "me vs. my wife" stage when our children were small so I completely understand your pain (this is to say that you are not alone and that many people go through that)

We first tried the "you are old enough to manage" which was of course a disaster. We then forced them to use a piece of paper but it was never clear who did what.

I ended up writing an app(I bolded the parts that in our case made a difference)

• that has an interface for each child and an administrative one for us
• the interface is very simple, but we did an important thing as we found out afterward: we added "fractioned chores" where due. Typically loading the dishwasher brings in 0.2, 0.50, 0.75 and 1.0 points. They are surprisingly honest on the fractions.
• the chores are independent, each of them has its own counter
• what constitutes a chore was clearly defined ("cleaning the kitchen means this and that")

The results are available on their app and on the home dashboard

The fun part of that added value, as well as the fact that there is a current count and clear "whose time it is".

This may not be relevant to you as the fun part when having very small children can sometimes be microscopic (but this will improve!)