What form should my Dad fill out to allow myself (his daughter) and his wife access to nurses to discuss status while he's in the hospital?

Usually during the admitting process this is done. Yes there is HIPAA form and sometimes the facilities own form.

I remembered when my Dad went into the hospital, the admin gave Dad a HIPAA form to fill out. Dad put my name and my Mom's name on the form.

Now, when my Mom went to the hospital, she wasn't able to fill out the HIPAA form due to her medical condition so my Dad, who was her Power of Attorney, filled out the form.

The hospital should have a HIPAA authorization for your dad to sign. That form will allow the hospital to speak to you.