Go to Settings->Facebook, And in the section labeled "Allow These Apps to Use Your Account" set facebook to Off.
The next time you open the App, and have logged out, you will be prompted for your password.
Alternatively, simply remove your account from that same location. This of course renders the Facebok integration inoperative. So you won't be able to interact with facebook from outside the Facebook App.
You can still access facebook outside of the integration. I do it all the time. You just have to do it differently. I choose to access facebook via safari so I can upload photos, comment on posts, etc.
THere are also third party apps that can be used to access facebook with a bit more control than the integration.
The facebook and twitter integration assumes that you want to be logged in all the time, every time and post anything and everything to their services.
The only way you can really control what you put on facebook or twitter is to not use the integration and use apps or a browser.
For your situation, try using safari and then tell it to not remember your passworld. That should force you to log in each time. If it won't remember that then use Safari and log out each time so you always have to log in.
Just to be clear, disallowing the Facebook App access to the Facebook integration account does not disable the integration. But does allow you to log out of the Facebook app without it automatically logging you on again the next time you open it.
Also removing your Account from the Facebook Settings page for Integration page, disables the integration, but does not stop you from using the Facebook App to access Facebook, and upload photos or videos etc... You simply can't post to facebook from the Notifications pull down, or from other Apps like the Photos App etc...
The Facebook website has been known to have issues in Safari. Also video playback can be a pain if it works at all in the browser.