How do I get my Mom to go to the doctor?

Use a "therapeutic fib" to get both of them into the doctor for cognitive/memory exams. You CAN do this if your PoA authority requires a diagnosis, otherwise how would the authority become activated? You can schedule an appointment for some other ailment they have and then go with your PoA paperwork, and a pre-written note requesting the cognitive test and why, then discretely hand it to the nurse before they go in to their appointments. Also request a test for UTI for your mom, since these are extremely common in elderly women and often the only symptom is changed behavior, hallucinations or confusion. Antibiotics can clear it up but someone will need to administer them to her so she takes her meds accurately.

You can opt for in-home aids for them but they may resist them and there's a labor shortage now. Plus this requires the PoA to manage this. Or, start visiting facilities to see which ones may be candidates. They can start with private pay and then apply for Medicaid, so only consider facilities that accept Medicaid.

Loneliness is brutal to the elderly and if you're in a rural area they may benefit greatly by being with other people, including a caring staff, in a place that has activities and distractions every day. Sounds like your mom may need Memory Care. Not sure about your dad. Wishing you wisdom and peace in your heart on this journey!

If you have POA and it is activated, she is already deemed unable to care for herself.vYou make an appointment and then invent a little lie about going to the store or out to eat (you can even do that after the appointment, so it isn't technically a lie)
and take her to the doctor.
Or get the doctor to play along with a different lie...like having her leg looked at for varicose veins or something relatively innocuous
Get creative but don't get permission, it won't come.
If you have a POA that hasn't come into effect, yet. You don't really have any authority to do anything. Except notify an aging agency in your area.

Tell her that "open enrollment" is coming up and that she needs to schedule a physical.
If she has a PCP if you can let them know in advance of your concerns that might help.
Good possibility that you can send a message in the Patient Portal. If mom has not set one up yet you can do one and you will be able to put in the correct information to set it up and set a password so you will have access to the portal.
Do make sure that mom has you listed on HIPAA forms giving the office permission to give you information.