Amazon.com: Woods 59203 Digital Lamp and Appliance Timer, Repeats Weekly with…
Looks like it should work for your needs, the battery back up recharges off the ac power, you should be able to find a 7 day or 5 and 2 day timers (week day, weekend) that has battery back up like that as well, $12 plus shipping.
If you find one that you like but that can't handle the amps, solid state relays seem to be pretty cheap, I have one that can handle up to 60 amps at 240 volts and I think it sold for about $10 but only works with ac because it closes it's contacts in the middle of the sign wave, when it's at 0 volts.