Why not have both GV/Obi and a Cellphone, and instruct the babysitter on both.
Or better yet, why not just hire a 24 hour paramedic and security guard, and then you won't need any phones at all!
To elikay: when talking about actual downtime, you are probably right. Between the modem, router and obi, you will probably have more downtime than your cell service overall. (Though both will be very minimal)
However, the main issue is not the downtime. The issue is that a landline phone is always docked in one area of the house, be it the kitchen, bedroom or other. And, it is powered by a cord, so is therefore always on.
A cellphone, on the other hand, is NOT. A cellphone can get lost anywhere and everywhere, and the battery can and WILL die. Not only that, but your battery charger can (and probably will) also get lost. (The response that "you can keep it charging at all times" is meaningless, because first of all, you will not do that, and secondly, a cell phone is not meant to be charging at all times, and it may kill the battery)
Even a cordless phone is more reliable in this respect, although it too can get lost.
Of course, nothing beats a solid, standard telephone line from a phone company (not a cable company) with a standard CORDED phone. A standard telephone line has its OWN power, so even in the event of a blackout, it will still work. (Cable phone relies on the modem, which relies on power from the wall. You can buy a battery for your cable modem, but it will only last about 10 hours) But even VOIP is a step above a cell phone.
Just trying to share some common sense here. I think those of you who have cellphones know how often you have a hard time finding it, or how often the battery is completely dead. (Oh, and how many of you power off your cellphones for Shabbos?)