In spoken language there's an alternate form which could sometimes be used to avoid such ambuguity. Of course, it's considered absolutely wrong (please, don't hurt me too much for even mentioning it) but in reality we all say such things from time to time:
I write poems, and then read to their mom --> Я пишу стихи, а потом читаю ихней маме
Also you can shift word order a little to prevent any possible misunderstanding, for example:
I write poems, and then read them to mom --> Я пишу стихи, а потом их читаю маме
So returning to your question, yes, there's some room for ambuiguity here, but typically the context is enough to understand it correctly. If still unsure, there's a plenty of variations to avoid any mistake completely.