As mentioned by sberman, no iPad released to date has an always-on display.
Recent models of iPhone displays can operate in an ultra low-power (always-on) mode - that reduces screen brightness and screen refresh rates. iPad displays do not have this capability.
While an iPad lack an always-on display, you can partially emulate this capability. You'll need to keep the iPad connected to its Power Adapter - and disable the Auto-Lock function to keep the display active:
Settings > Display & Brightness > Auto-Lock - set to Never
You'll need to keep the iPad connected to external power as otherwise the iPad's battery will be fully depleted within hours. Older iPads with older batteries will inevitably have much lower charge capacity than newer devices with fewer charge cycles.
However, you should be mindful that the iPad will be accessible to anyone that has physical access to the device. By virtue of being always unlocked, this can expose personal or sensitive information either stored locally on the iPad, or stored/synchronised with the associated Apple Account.
As such, you might be wise to reconsider displaying your Mom's calendar or any other personal information. If you instead create a new and entirely separate Apple Account to be used with the old iPad - that is not linked to your Mom's account or associated personal data - you can still show date/time, weather and other generic Apps/Widgets without risk of compromising personal security or privacy.