My first thought was
- Develop a way of working that allows you to very smoothly 'save your state' and resume it;
- Divide your time into small chunks (how small is To Be Determined);
-
Find things that you can do with the kid with full attention that fit into a chunk;
- Find other things that the kid can be given to do in your space that occupy them, that also fit into a chunk;
- Alternate between the two states of $working and $parenting.
- and then veg out with a nice glass of wine at the end of the day
I then read the OP to my wife (she works as a psychologist partly at home, while I work as a developer-consultant mainly at home but only started doing that when our kids were in their teens).
She simply said "You don't." Your time must be either fully one or fully the other, and while you are 'at work' the minding has to be down to some other adult.
This signature was ready by Christmas but it broke