I just got turned on to the Workbox System and I think it addresses all of the OP's issues/concerns.
From my own experience of having been home schooled, I definitely think that structure, in a positive frame, can work volumes. If you are concerned about character, my honest opinion is that if you are failing in that area, they will understand better when you confess it to them and tell them what you are going to do different and stick with it (easier said than done, I know). I personally think that character development takes time and immediate results aren't necessarily the ones that speak to long term growth. Character takes time to develop. I'd much rather hear from my child's Sunday School teacher that he is polite and inquisitive and (fill in the blank) than otherwise, even if he's acting out at home. I've been told countless times that children are vibrational sponges and they act, in part, the way they do at home because in some way they are trying to communicate a need that isn't being met and that they don't yet have the maturity to speak into that issue and bring it to light in an adult way.
I don't know what I"m going to do when my kids are the ages of yours... so all what I'm saying is just my thoughts. Pray for grace. Constantly. And mercy. Because it's impossible to think or expect one, imperfect, though justified and continually being sanctified, human being, to parent another imperfect human being without the proverbial bumps in the road.