If my daughter fell on my sister's stairs, can I sue her homeowners insurance company?

First, be aware that you do NOT sue an insurer--you sue the homeowner, your sister. You'd have to file a lawsuit against her, and if you won but her insurer had some grounds to not pay (e.g. she was late on premium payments, or didn't comply with policy terms), it would be your sister who owed you the money. Or if you won more than her policy limits, she would owe you the balance.

Second, for you to have a claim against the homeowner, the homeowner must have done something wrong--a person is not liable for injuries which occur on her property simply because they happened on her property. If the stairs were in bad repair and unsafe, or your sister or a child of hers pushed your daughter, or someone left a rollerskate or skateboard or ball on the stairs, etc., then there would be grounds for liability.  But if you daughter fell on stairs which were in reasonable repair without your sister or her family having done anything wrong, there would be no grounds to recover compensation.