Wi-Fi Analytics Tool should allow you to change channels, but I don't think that's your problem. I suspect it's a bad router. (The tablet, if it's connected to Verizon, gets its time from their towers, which shouldn't be as much as a second off (since it's GPS time, that would be a monumental failure for the entire world, including the US military) - as long as the time
zone is set correctly. Or it could be a flaky Wifi transceiver in the tablet. Wi-Fi Analytics Tool will tell you if the router is flaky or not - that's he first step.
The second step is to turn off security in the router - no WEP, no WPA, set it to be open. Then you're dealing with the same thing as a public network. If it still doesn't work, it's still probably the router. If it does, pick a security (SPA2 Personal with AES encryption is just about universal, and more secure than TKIP) and see if that fixes it.