Homeschooling in a daily routine

Yes you may. The neologism “homeschool” as a verb is now well understood, does not replace any previous word unnecessarily, and is concise. There are therefore no arguments for not accepting it into usage.

Your use of “must” clearly depends on the circumstances but whether or not or why you are obliged to (must) finish the task by a particular time is irrelevant to the thrust of your question and to this answer.

To homeschool seems to have a unique meaning: to provide one's children or someone's chilren with an education through private tutoring (wiktionary).

• To educate children at home, that is, at a private domestic place, in lieu of sending them to a public school or private educational institution.

It does not mean "to teach homeschool" nor "to give lessons in the context of homeschool"; I find those definitions nowhere.

To say for instance "four days of the week he teaches school to young children" in the context of homeschooling you'd have to say "four days of the week he teaches homeschool to young children".

For instance, taking the verb "to school", two definitions exist.

• 1 (formal) to train somebody/yourself
• 2 (formal) to educate a child

Note that using the verb in "2" you can't say for instance "She is schooling this child with the others this morning".

It would probably be better to say "by 3.00 p.m I must have finished teaching my kids", thus preserving the existing model. It might be understood by a sharp enough listener that you are an adept of homeshooling.

Another possibility: by 3.00 p.m I must have finished giving my kids their homeschooling lessons