correct phrasing

Yes. It is perfectly normal.

Thanks, Contrex.

Excuse for asking such a simple question but, being a perfectionist, I will ask any question in which I've doubt.

It's perfectly normal and correct in colloquial speech. In very formal English many traditionalists would object to it, and would prefer some other construction, e.g.:

I feel that we are one big family.
I feel as though we were one big family.
I feel as if we were one big family.