My Internet constantly disconnects and reconnects to another network that is not ours, what is the problem?

My Internet is fine at times and then randomly disconnects at other times. I have called my Internet provider and they assure me that it isn't them however I don't see how it is me. My current solution when the Internet goes off is to get up and turn off the router and turn it on again, however sometimes it turns off before you sit down again. When it disconnects it sometimes reconnects to another wifi connection that is not our which we cannot use. Can our Internet WiFis be competing, finally I dont know of this means anything but it sometimes disconnects when other people try to connect to network, please help any ideas are appreciated.