Hi N.
Sounds as if you are a very busy productive mom.
Sounds also like you have a daughter who is willing to do preschool some of the day. That is very exciting, some will indicate preschool for children and I taught there. There are drawbacks. With the twins I set my day up to do preschool with all the preschool activities including calendar time, which teaches numbers, months, days, weather, appropriate clothing and anything else you want to include such as moon, and planets. You mention academics, but puzzles and playdough are done in preschool, along with music(instruments, and band, as well as types of music itself(patriotic, gospel, folk, etc) plus learning the words is great memory skill if they are done as a fun activity they can develop a life long love.
Don't forget listening & picking out what instruments are playing. There are also sounds we hear(train, siren, hammering). Naming them is also fun. Games, & physical activity(jumprope and bouncing balls) Baking cookies etc is also fun and a great way introduce fractions so they don't seem so overwhelming when kids are introduced to them at a later age.
All of these things take time to plan, and you to be there interacting, so don't forget quiet time, that involves her thinking of things to do. I called it recess, which some call quiet time or naptime. Mine never liked naptime they didn't want to sleep, and we were not sure we wanted them to. Recess was good, and I let them play as long as they were being good and thinking of constructive things to do(dolls, blocks, lego's,or imagination play(dress up) A good preschool will do all these things, but you have no control over who is in the room. I am not much of a person to say your child needs preschool.
I am not much into passive entertainment, and not much into computers as entertainment, however, AOK with them as learning tools guided by adults.
20 minute time slots are good, unless otherwise dictated by your child.
God bless you with wisdom and strength. Parenting takes more energy than any business. I can see you spend much time at your business. I know you will invest time in your daughter as well.
K. SAHM, taught preschool some then decided to homeschool. Married 38 years, adult children 37 coach, 32 lawyer, and twins 18 who left for college last fall(they are waiting for grades each with a goal of 3.5 or better in each class, both were able to opt out of two exams because of having 4.0 in the class--they are in different schools 4 hours from each other) after years of homeschooling. The average public schooler gets about 3 hours of actually in classroom study time each day, which means with planning if I homeschool 8-12 which I did for years without interruption(that would be rare in public school) I have taught an hour more than the school and we have the afternoon to do other things.