My response is a little different--and is not meant to be harsh in any way, but to appreciate your sense of being overwhelmed.
Let yourself off the hook! Your DD's are blessed to have such a caring, supportive mama. The fact that you care, that you are willing to give so much of yourself, that you want to be there and "get it" for them--that is more than many kids ever get.
Like BirdGirl said, kids (especially gifted kids) will always find ways to learn. They can't turn it off. As they get older, they will find more and more ways to seek the knowledge they crave on their own. You don't need to take responsibility for all their learning and exploration--just help them access the tools/materials they need.
It sounds like you are carrying a lot of worry about offering the kind of support to your DDs that you did not get yourself. The desire to give support and understanding is great--it's what I wish I had growing up, and what I want to give as a mother. It's the worry you can let go of.
It seems to me that most moms spend an awful lot of time worrying about whether or not we are good enough mothers. (Do I spend enough time with my kids? Do I have enough patience? Do they get enough stimulation? Do they feel loved and challenged and appreciated?) I know I have spent many a wasted night fretting over it all. In truth, anyone as thoughtful as you are is a plenty good enough mother--and your DD's are lucky to have you. So, stop worrying and just love them.
This is not meant to undercut the challenges you face, especially with special issues with DD2. Mothering is hard, and gifties can make it all the more intense. The emotional sensitivities (and probably your own strong sensitivity and intuition) put you in tune with every small hurt and frustration. But, like you, your DDs will need to grow and learn to cope with their own emotional sensitivity--to feel deeply and passionately life's disappointments, frustrations and limitations, and find ways to respond. (I'm thinking about the incident with the bikes.) It's hard on everyone, but they will be fine.
It's okay to have limits with what you can and can't do, even though you want to do it all--you are teaching your DDs that the world as it is is not the world as it should be, but we do the best we can. You do the best you can as a mom. That's all anyone could ask. Much as we would like to, we cannot do everything we want to for our children. But even if we could, I'm not sure we'd be doing them a service, because the rest of the world doesn't work that way and they would come to face it unprepared.
So, good for you. You care, you love, you listen, you support as best you can--which sounds pretty good to me. Let go of the worry.