are you saying your plugs and switches are turning on too?    sorry, but as far as I know, that cannot happen.   Power outages would turn off plugs and switches.     

After a power failure, even a second, Alexa turns on lights, etc. How can this be stopped? lights don't need to be on while away or asleep. Two of the three units are on a battery backup.

it is hard for alexa to tell the difference between a power failure and flipping the switch.   You did not mention the brand of the bulbs but if they have their own app, you can see if there is something about restoring to power state or something similar.   If not, you are out of luck.    I cannot say the number of times I come home and the house is lit up like a christmas tree after a power outage.     You may be able to set up a routine that if a certain bulb is on, to turn off all the others.   The only other option is to switch from smart bulbs to smart wall switches and smart plugs.   

After a power failure, even a second, Alexa turns on lights, etc. How can this be stopped? lights don't need to be on while away or asleep. Two of the three units are on a battery backup.

You have to start at the far end and work your way forward.

1. You need two, separate, Amazon accounts (different email addresses)

2. If the Dots were purchased at the same time, from one account, they were probably preloaded with the details of that account, so you would have to de-register that Dot from the first Amazon account then perform a 'factory reset' on the Dot you're going to move to the alternate account.

3. Make sure the Dots are not on the same network at the same time during set up (ie: unplug the first Dot) and then set up the second Dot (the one that has been reset) with the second account.  This means the Alexa app on your phone/tablet has to already be logged into the second account.  Once things are set up in each Dot you should be able to run them on the same network.

Hopefully, this helps

Kyle

using apple or android?