Can't share my card with family members, have to buy everything twice I am a "family organizer". The card is set to be shared with the members of the family.

Yet everybody has to use my account. Just tried it with my wife, urged her to login as herself (App Store asked her for the credit card). Then she deleted Keynote that was purchased on mine account, clicked Buy and my card was billed additional $20.

What is going on here? I have a big family I don't want everybody to use my account.

I have the latest everything. The family is set up, we are exchanging photos and videos since it was released. Shared payment method is set up as well and yet it charged me again.
You shouldn't need to pay for other family members to download the app, provided you all are running the latest iOS software (I'm not sure if it requires iOS 9), iCloud Sharing should allow purchases to be shared between six family members. See http://www.apple.com/icloud/family-sharing/ for information and https://support.apple.com/en-us/HT201088 for help setting it up.

You can go to the receipt Apple will send you for the $20 Keynote purchase, and there will be a link in there to report a problem, and you can indicate you did not mean to purchase. It will hopefully result in a refund.