Hi Dave:
OK, holding my breath here, as the classic scenario on this forum is that you'll get a cluster-f__k of replies, with detailed digit maps and related technical tweaks to potentially make your proposed solution work, after many back-and-forth reply posts.
Having worked with seniors to assist with their daily living issues, and um, being one myself, I would instead look at the bigger picture: it's most important to consider safety, simplicity and reliability.
There's nothing wrong with porting your mom's phone number to either Google Voice or a SIP VoIP service provider, and then she can use that as her primary line for inbound and outbound calling. See the FAQs for a guide on porting a land line into GV if you choose that option, or pick a reliable SIP VoIP ITSP, like Callcentric,
voip.ms, Phone Power, etc.
However, I would recommend against trying to integrate the cell phone via BT, as it may just end up creating upsetting issues when things don't work. Consider: the entire home network, not just the OBi, would need to be on a UPS (cable or DSL modem, router, OBi, phones, etc). The OBi-->BT solution might not work in an emergency, causing risky delays in reaching help on the phone. At some point, in an extended power outage, the ISP connection to the house will go down, and I doubt there is a reliable way to intelligently detect that and fail over automatically.
Instead, I'd simply give her the prepaid cell phone, leave it attached to a charger, and tell her to use it in case the cordless phones aren't working for any reason.
Less technical complexity = more reliability and less anxiety-production = happier senior.