@alexandra123
In order for your mother to open an account, she must be in a position to assent to its opening, even if this is non verbal. Assuming that this is the case, given that she is not a Ward of Court and you do not mention having an EPA for her, I'd suggest proceeding as follows:
Break this up, into two parts:
1 - Opening the account: Send a letter (by registered post if you want to avoid time wasting and show you are serious):
The Manager
XYZ Credit Union
Dear Madam/Sir
My elderly mother wishes to open an account with your Credit Union. My mother's communication is limited as she does not speak and does not write. I assister in personal and financial matters.
In order to facilitate this we would request a meeting with you in a private area in your ABC Branch at 2.00pm on Friday 22nd March, or at such other time as suits you - please give seven days notice.
My mother will bring her passport and two utility bills with her on the day. If anything further is required please let us know in advance. I can provide all the required information on the day and my mother will nod her ascent.
You might confirm the above appointment at your convenience.
My number, should you wish to contact me is xxxxxxxxx. Best time is weekdays from 9am to 1pm (or whatever)
Yours faithfully
Take €100 with you as an opening balance. Once you meet them they should be able to open the account there and then.
2. Once all of that is done, introduce the issue of the insurance policy. It may be that the monthly premium has to come from your mother's CU account. If this is the case, you can transfer money into her account monthly or from time to time to meet the premium due.
One thing to check in advance - not all Credit Unions are affiliated with ECCU, and not all of those that are offer the insurance product, and of those that do the terms and conditions can vary. You're sure that your credit union offers the policy you refer to ? (Not doubting you, just trying to avoid confusion)