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