Be aware that if your mom is not competent, she can't sign a power of attorney. If she is still competent (but needs help) then you should fill out and both sign IRS form 2848. Of course the IRS has their own POA form, because that's how bureaucracies work.
https://www.irs.gov/forms-pubs/about-form-2848
If she is no longer competent, the IRS still wants you to fill out as much of form 2848 as you can, and attach a copy of the actual POA form.
If she is still competent but needs help, she can e-file her own return (i.e. she can sit with you when you file and give you her verbal consent while you actually push the button.) If she is no longer competent, the IRS wants to you file on paper, sign your name as "personal representative", and attach form 2848 (with a copy of your POA) instead of e-filing. You could probably get away with e-filing as long as you know her AGI from last year so you can get through the e-filing interview, but it is not technically correct.
As stated, you are still required to file even though you are late. There is no penalty if she is due a refund. If she owes taxes, the penalty for late filing is 5% of the amount owed per month for the first 5 months that she is late.
