I know I can say:
- There is a group of 4 girls standing on a bench.
How about this?
- There is a family of 4 people.
or
- There are four people family.
Is there the best option other than these?
I know I can say:
- There is a group of 4 girls standing on a bench.
How about this?
- There is a family of 4 people.
or
- There are four people family.
Is there the best option other than these?
Yes, "There is a family of four people" is fine. In fact, you could even exclude "people" and it would be fine, as it is implied that the family is comprised of humans. I'm going to include the rest of your original phrase because it makes the sentence make a little better sense. It's not wrong without it.
There is a family of four sitting on the bench.
This will pretty much always mean that the family is all present, sitting on the bench.
Your third sentence is a bit more complex. There are a couple of options here but I would say, as is, it's not a good construction.
There are four people family.
Option one is to add "in that/this" to the sentence:
There are four people in that family sitting on the bench.
This sentence can be very ambiguous. If said aloud, the stress put on different words can make it less ambiguous. There are three things I can think of it meaning:
Option two is to make "family" singular and turn "four people" into a modifier of the family. When you use "four people" as a modifier of "family", it should actually be "four person" or "four-person".
There is a four-person family sitting on the bench.
This means the same thing as the original sentence, all four members of the family are present and sitting on the bench.
Sentence number 2 is correct to use but number 3 isn't. I believe that your second sentence could cause confusion to become as a question. So, I recommend you add a place at the end of it. For example:
There is a family of 4 people sitting on a bench.