Not sure if this is the right forum, however we have 2 echo dots and they both just have a green light that pulses on and off constantly on them? I've tried restarting them and they just do the same and there is nothing wrong with the internet as everything else in the house is ok.
The green light as far as im aware means drop in is active. so you can say for example drop in on kitchen and speak to someone on another device in the house but not sure why it would go straight to that! Try Saying Alexa/Echo hang upor stop.
If theres a problem with connection with would pulse red
Try announce! For example if you have one in the kitchen, while the wife/missus is in the kitchen say something like "Alexa announce make us a brew love' it will announce it on all devices but she wont be able to reply as its just an announcement.