By process of elimination, if your situation is neither of those above, you probably want 'their.' You've tipped the odds of a guess in your favor by using the two tests above.
But, to be thorough:
Their -- shows possession. If something (an object, an idea...whatever) is owned or held by a group of two or more people that doesn't include you, describe it as theirs. The test here would be if you were talking about a group that DID include you, could you replace 'their' in the sentence with 'our' and it would still make sense? If so, 'their' is the choice you want.
Marsha, Jan and Cindy usually sided with their mom when there was a disagreement with the men in the house.
If you imagine for a minute that you are Cindy, the sentence would make sense reading, "Marsha, Jan and I usually sided with our mom when there was...."
This is a slightly more complicated test, but not really difficult once you make a habit of stopping to check that you've chosen the correct homophone (words that sound the same) when writing there/their/they're.
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