[matzek]

Do you know of a device which will connect a modem to two phone lines, and will either fail over to the secondary line or allow remote switching from one line to the other?

[lukenysen]

AT&T use to make a device allowing single-line phone devices (such as your modem) to switch between two lines, but this had a manual switch. There was no way to operate it remotely.

I've kept my eye out for similar devices since then, but I haven't found anything to date. I don't think there's anything of that description on the market, but if you find it let me know.

The next closest category to such a product are line-SHARING devices. They direct INCOMING calls to the correct device (phone, fax, or modem) by detecting special tones.
http://www.evaluezone.com/multilinkstick.html
But it doesn't sound like this will solve you're problem.