Yes, your mother can apply for a non-contributory pension.
The non-contributory pension is means-tested, so household savings, income or property (other than the family home) will be assessed as means.
Your father may already be getting a payment on his state pension in respect of your mother (called an Increase for Qualified Adult).
Now that your mother is aged 66, that payment should be increased (the max rate for a Qualified Adult aged 66 or over is €206.30, for a Qualified Adult under 66 it's €153.50).
If your father applied for his state pension after 27/9/2007, the Qualified Adult increase is paid directly to the qualified adult, instead of the pensioner.