While my older daughter was a super easy baby and toddler, and I was able to do pretty much everything (we even ran and doubled in size a local chapter of a national networking organization), the little one has different requirements.
She loves a lot more physical contact, undivided attention, and sitting on my lap is one of her favorite things to do. She couldn't care less if I have work to do. So, one thing that enables me to respond to emails and get some work done while snuggling with her, is my desk drawer.
In that drawer, I have all sorts of stuff for her to play with: old business cards, puzzle, washable markers, and more... That way, she can explore and is pretty content while I work on non-client related work.
Some other ways to keep the little ones engaged are:
keeping special toys on hand that are only given to them during phone calls.
when they are a bit older, assigning them simple tasks that they work on while you're working on yours.
spending really quality time with them right before an intense work
session, and right after. (Setting up timers to stick to the promised
time frame works great).
I would love to hear what are, or were, some of the ways you combined parenthood with entrepreneurship when the kiddos were at home with you?