As a general statement of truth, there are any number of ways to express this thought. However, some are better than others. In your second sentence you say:
When you get family ...
and while this is an interesting phrasing, it doesn't really make sense. You don't get (in the sense of acquire) family. Your family gets you.
Instead you could say something like:
Where there is family, there is drama.
This expresses the universal truth that the existence of one inevitably leads to the existence of the other.
In a similar way, "have got", as used in your first example sentence, expresses the existence of something rather than the acquisition of something. An example:
I've got two brothers.
I didn't acquire my brothers. My parents (obviously) did that for me. Have got is another way to say exist.
Note you can also use have instead of have got.
I have two brothers.
Although this implies more possession than acquisition, again it actually means they exist (since I certainly don't own my siblings).