How do I disable GMail? Yes, this has been asked before, but neither really addresses my concern, and I don't have reputation enough to add comments to existing questions.

I've bought the cheapest Android 4 tablet with Google Play that I could find to have a device in the kitchen that syncs the family members schedules and displays them all in one place, edit shopping lists that sync with my mobile, shows the recipe I'm following while cooking etc.

As all family members are going to use it, I want syncronization of calendars, and I want to use my Google-account for which I have already purchased apps for my phone as the Google account in Google Play on the tablet, but  I do not, however, want the whole family to be able to access my email. So how can I turn off Gmail access?
As noted in the answers to the questions you linked to it isn't possible to just sign out of the Gmail application and not other Google services. 

In order to achieve the functionality you want though have you considered using an application lock such as APP Lock? With this you can require a PIN to open the Gmail app. Whilst it doesn't turn off email access it will prevent the whole family from being able to access your mail.

N.B. If you have kids using it as well then it might be worth requiring a PIN in order to purchase anything on the Play store, this might prevent some nasty surprises appearing on your credit card bill. You can see how to do this here.