It is my understanding that it is not so easy to open an account in Bali as it once was.

I was thinking that opening an account in your own country, and give the ATM card to your Bali family. You will of course have to make a minimum deposit to open the account that you may not want your family in Bali to have access to, that I believe would need to come under the catagory of communication and trust. You would be able to add funds as needed and the only fees that you'd incur would be for the use of the ATM and any charges from your bank for ATM usage. I've noticed that credit unions have the lowest charges..