Solution to the problem (problem may be with installation of non-default launchers(For me it was Kid Mode a game for my kid))
Step 1 -- Intentionally put in the wrong password to access the router..
..it will of course fail...
Step 2 -- Put in the correct password.
It will reconnect like new.
This is what worked for me, and if you have the same problem (really no matter the Samsung device) it should work for you.
For whatever reason putting in the wrong password makes the device actually attempt to connect again. I had tried everything from placing the device on the router, resetting the router, restarting the devices, removing apps, factory resetting one device( which worked after two resets on the non-stock Vibrant), forgetting the network, turning off sleep mode in advanced wifi settings, adjusting all sorts of other settings.
Thought I would share my solution and I hope it helps more than just the Note 10.1 community if this occurs to others, which my google search results showed me it does and on many Samsung devices...which makes me sad, because I love my Samsungs.