They is nominative case. However, here you're using it as the object of a preposition (
between), so you need objective case (
them or
themselves). That means
they is wrong.
Now,
them or
themselves? Since there are a limited number of situations in which a reflexive pronoun can be used, it's usually easier to check for those first. If none apply, then the simple objective
them would win by default.
The reflexive pronouns are:
myself,
yourself,
himself,
herself,
itself,
ourselves,
yourselves, and
themselves. There are three main situations in which they are used:
1. When the subject and object (of the sentence) are the same.
Ex. You shot yourself.
2. As the object of a preposition, referring to the subject of the sentence.
Ex. He read silently to himself.
3. To emphasize the subject. (OK, technically, this is intensive, not reflexive, but they're all the same, so it doesn't really make any practical difference.)
Ex. I tied my shoes myself.
So does the sentence in question fit any of those? Yes, it's the second one. You have the preposition
between. The object of that preposition is
[them or themselves] and their guests. (By the way, even though it's a compound object, you need to look at each part as if it stood alone.) The pronoun refers back to the subject of the sentence,
the women, so it has to be reflexive.
Therefore, you need to use
themselves.
