how to give up authority effectively and still be in-charge

I work as an IT consultant, mainly in BI services. Means I study market trends for whatever I work for and see how their current IT system uses those trends to do analysis, how to improve that system and how to get reports that actually are easy to use. So that means I'm a 28 year old who goes around telling older people "yeah well your way sucks, this is how you do it" A LOT! (I say it in a much nicer way; my mama taught me wonderful manners)
And I also own my own Montessori so I'm in charge of 12 teachers and about 50 kids aged (0 to 13).
Some days are easy; others manage to suck the life right out of me. But anyway, back to the point.
Point is : I'm in a position of a boss, team lead, and a project lead a lot. Initially, I thought if I let someone else do it, why will anyone hire me. But I started getting burnt out and resenting waking up.
I learnt this: to be a good leader you have to delegate tasks to the team. But delegate based on the skill set of each team member. And have daily 10 minute face time with team members to make sure you are all on the same page.
Also, never directly put down anyone, get someone else to deliver the bad news. Because trust me 'everyone shoots the messenger'.
And most important always use the 3 strike rule; that means 3rd time anyone (and I mean anyone) screws up on the job you cut your losses. It keeps your team on its toes. It sounds harsh but Bill Gates used to yell at people at Microsoft if they messed up; if you read about Microsoft you will realize it was a high strung work environment.
Also you know how your mama always says "learn to pick your battles". Its true. This applies to life and work, pick your battles wisely, sometimes an issue or disagreement is not worth acknowledging.
I say this a lot at work "and i completely agree with you." But honestly, I don't completely agree ever (just ask my family). But sometimes it helps to settle down the team and just push to get the job done and deliver the milestone.
All work battles should focus on making the company succeed in the project. Work battles should never be about your ego or your pride. Learn to be humble and leave the cocky attitude for happy hour or for when you get an achievement award.