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If I can say
Su madre busca a su hermana.
to mean
Your mother is looking for your sister.
And "su" can also be used to mean "their", then what if I want to say "Your mother is looking for their sister"? Because if "su" can be used for his/her/their/your (formal), then it leaves much ambiguity in this example.
Indeed Spanish has that ambiguity (it would be hard to find a language without ambiguities).
As you can see here, it is as you say. If you want to say
"Your mother is looking for their sister"
you say it
Tu/su/vuestra madre busca a su hermana.
You deduce from the context which su is meant in the sentence. If a risky misunderstood could arise use the (I'd say not so elegant) variant
Tu/su/vuestra madre busca a la madre de ellos.
If you are saying your mother it will be very rare that you would use "su madre" because "su" is for the 2nd person "Usted", and that puts the sentence in a very rare context, talking to someone with a lot of respect and talking about his/her mother, not saying it's impossible but it will be very rare. If you fall in ambiguity you can add what's necessary to remove that, but I think the context could help, maybe while you're talking to the person who's mother is looking for the sister of the other people, you could point or make some gesture that can help you, remember that the bodt language is also very useful, anyway it could be like this:
Your mother is looking for your sister.
Tu madre busca a tu hermana.
Su madre busca a su hermana.
Your mother is looking for their sister.
Tu madre busca a su hermana.
Su madre busca a su hermana.
Vuestra madre busca a su hermana.(old-fashioned)
Tu madre busca a la hermana de ellos/ellas.
Su madre busca a la hermana de ellos/ellas.
