I am very sympathetic for practices who elect not to accomodate emergency appointments where they have no current availability. Because while its a very nice thing for the patient in need, it disrupts everyone elses appointments. Ultimately I prefer knowing my time will be honoured, than turning up and aiting or being cancelled on.
As the person in need, you did the right thing. Your dentist could not accomodate, you did not wish to wait, and you found an alternative solution. Perfect.
How you travel forward from here is completely up to you. You have no obligation to either dentist and you should contiue with who makes you feel most comfortable.