Dear Busy Father
Ashrecha that these are the issues that concern you! Your children are fortunate to have such a father and you are fortunate to have children that wish to learn with you.
The Mitzvah of chinuch is no different than that of lulav, or shofar or krias shma, in that you must properly fulfill your obligation. Chinuch is trickier, because there is no prescribed 'shiur', and whatever will have the most positive impact on the child is recommended. Older children can perhaps appreciate the fact that you are learning, and may even be be inspired by your example, but for younger children, you should enjoy the opportunity to learn with them whenever they are willing. (With an older child, why not invite him to join you in Daf Yomi?)
An experienced mechanech that I discussed this with suggested that you make your set learning time outside of the house, perhaps in the early morning or late at night.