You already know what I think about dating while married... It is a huge 'no, no' and it is unfair to you, your W and whoever you date.
If you really want to date and think your M is over, get a divorce, have a mourning period for the M that was (takes anything from 6 months to 2 years by what others tell me), then date to your heart's content... after having analyzed what went wrong in your first M and how not to fall in the same trap twice.
You do not need to date to show to your W that you can move on: she knows well that you are more responsible and better organized than she is. If you date now, you only 'show' to her that you did not really cared as much as you said you did.
Sorry, I go with the majority opinion. Whoever gave you that advice has very good intentions but very little insight into female psychology...
"You don't throw a whole life away just 'cause it's banged up a little"
Tom Smith in "Seabiscuit"