Outgoing e-mail blocked and also can't add a cox e-mail address to gmail

Problem number 1:  I keep getting error messages over the last few days regarding e-mails I have sent that say:

Delivery to the following recipient failed permanently:

     [e-mail recipient's e-mail address here]

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the relaysmtp.cox.net [68.6.19.8].

The error that the other server returned was:
535 5.7.0 ...authentication rejected

Cox told me to re-set my password, which I did.  Did not solve the problem.

Problem # 2:  I use gmail exclusively, and send cox alias emails through the cox server.  I deleted one of my cox emails from settings in gmail, and now I can't re-enter it because I get the following message from cox:

Your other email provider is responding too slowly. Please try again later, or contact the administrator of your other domain for further information.

I see lots of other people have had these two problems, and after three levels of cox support cannot offer me any solutions, I'm here to see what you all have done.