Homeschooling can be great, but if you're current situation is working, why change it just because you feel like you should be homeschooling? If you do decide to homeschool, do it because you really want to.
I really wish pedis would look at the child, not just the numbers. I have the same problem regarding my oldest. He's got a 6-pack and you see the muscles in his back at 6 years old but the pedi says he's obese. Your DD looks fine and I'm guessing she'll shoot up in height fairly soon.
No, I don't tell any of my children to keep their legs closed. If you can see DD's underwear, its probably because that all she has on. I'm sure this will change as my children get older but right now I'm not at all concerned about my 4-year appearing "ladylike."
I think its a consequence of having more then one. I slowed my response time with each one. I don't believe that a minute or two while I finish something equals CIO. Especially, if that something was a quick bite or going to the bathroom.
Can you move his quiet corner to a more central location in the house? So he's not so isolated? Later when he gets better at self control you can move it to an upstairs hallway and then to his room.
Is he getting enough 1:1 time with you? I know its hard with a new baby (been there, done that) but more time with you can help prevent some of these meltdowns. It made a world of difference to my older kids when I would put the baby down for a nap instead of wearing...