In Live Chat 3 - Version 3.2 we added a feature to change the floating button position for each chat widget straight from the operator panel.
Go to your operator panel - chat widget - select a chat widget and you will see a new input field.
You can now place the button wherever you like to suit your design. You can play around with following values:
top, bottom, left, right
For example you would like to place the button on the top / left:
The value above will place the button on the top / left with 20px space from the window border. Of course you can change it to any value you like.
This time the button will go to the bottom with 40px space to the window border and with zero space to the right.
Important: when using the floating button always have a value set where you like to have the button placed.