Our old savings account has earned bank interest. What should be done with that money?

Riba interest may not be used for oneself; the widely held view is to channel it to public benefit, such as through the Baitulmal, without the intention of charity for reward.
Allah says: if you repent, you may have your principal; you will not wrong and will not be wronged (al-Baqarah 2:279). The verse shows that what is rightfully yours is the original capital, not the added riba. Since the original owners of the interest cannot be identified, scholars advise channelling it to general uses such as public facilities; in Malaysia, some state Islamic religious councils accept non-Shariah-compliant money through the Baitulmal. For the future, move your savings to an Islamic banking account. Do not use interest money for the family's maintenance. Ask your state religious office or Baitulmal how to do this. See the question on riba and financing.