The Grandstream HT502 is your ATA; you can connect just about any regular phone to your ATA. I would recommend something like this
, a corded/cordless handset. The corded handset doesn't run off of battery, so it can be used for those really long phone calls, while you still have the convenience of a cordless handset for all the other calls.
The limitation of the corded handset, though, is that the wired handset would need to be located next to the Grandstream, where your Philips base station is now. In exchange for unlimited talk time, your mom-in-law would be stuck in the computer room for the duration of the call.
The other option, is simply to continue using cordless handsets, and switch handsets when the battery on one gets low. This wouldn't give you unlimited talk time, but it would significantly increase the maximum length of her phone call.