2 iphones, 2 computers and 1 itunes account

" If I buy an app will it show up on her computer too when she revisits the itunes/app store?"

No. She may be able to re-download the app for free, The same is not true of music.

http://support.apple.com/kb/HT2519

You can authorize up to 5 computers on 1 iTunes Store account. This means that you could use two computers with just 1 account. If you choose to go this route, she won't automatically see everything you buy, but she will see notices when there are updates for the apps. Similarly you will get the same for everything she buys. One side note, if she tries to buy an app that you've already bought, it will tell her that she's already purchased it and ask her if she wants to re-download it for free. Unlike music, you can re-download apps for free once you've purchased them.

You can sync as many devices as you want to your computer, although there may be some limitations on how many of a certain type may sync at the same time. I have had 2 iPhones and 2 iPod Touch devices all sync to my iTunes install on my computer. I know that you are not asking about syncing both phones to the same PC, but it is possible. Each device can sync to it's own computer with no problems (even if they are using the same store account). Both my wife and I use my store account on separate computers, she managing her own iPhone and iPod Touch, and me doing the same with mine. This would be the scenario you are describing with your daughter, other than that your two computers might not be in the same house.

Just treat each computer like a stand alone iTunes install with it's respective devices. When you get to the point of logging into the store account, just use the same account login on both computers.

Yes, if the computer are on the same home network, which it seems they won't be.

You would have to copy the file and get it to her to copy to the other computer.

Greekboy: My wife and I have a similar arrangement with our iPhones: two phones, two computers, one iTunes account.

However, I cannot help but wonder why you would have both iPhones and iTouches. Just curious.