What's the correct construction and why?
Since there was/were only a couple and two families, she had the freedom to choose her seat.
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Does a couple and two families sound like something that's more than one? It certainly does to my ears. Only there is just an adverb and has no effect whatsoever on the grammatical number of the phrase a couple and two families which is the subject of that clause. And since the subject is a plural thing, you should use were to make the copula verb of the clause match up the subject in number. Yes, with constructions like there is/are or there was/were, the subject comes after the verb and not before it as is typically the case in English. When there is used like that, it's called a syntactic expletive:
A syntactic expletive is a word that performs a syntactic role but contributes nothing to meaning.
In general, the usage pattern for the expletive pronoun there looks like this:
there is/was [singular subject] there are/were [plural subject]
There were a boy and two adults in the room.
There are an apple and a cup of tea on the table.
However, note that in everyday spoken English, while grammatically wrong, native English speakers many times would use the singular there is/was even in situations when the subject is plural. For example: "There was 30,000 people at the concert", There's two people waiting for you in the lobby. This is so common that using there is/was with a subject that's plural is basically considered the norm in conversational English. Why that happens has probably something to do with he fact that there's and there was are phonetically faster and easier to say than there are and there were. But that's just my guess.