Your cons jump out at me.

You're not sure it's going to be socially advantageous to go to school, so that negates one of your 'pros'.

Driving is going to really wear on you, taking away time you would like for yourself.

You are worried you are not giving DS3 enough time, will sending DS6 to school give you more time with DS3, or will it just cut back on time with DS6 and relieve guilt for not being 'fair'?

You enjoy homeschooling, your DS6 is doing well with it and wants to continue. I think your major concerns are getting enough time for yourself and with DS3. What about a home daycare provider for both boys half days, several days/week, so you can get free time, and DS3 continue preschool another year half days?