What is the differences in nuances between とうとう and やっと?
is it true that やっと has a more "happy" feeling attached to it?
やっと means that something realizes after spending/waiting a long time for it or making a lot of effort for it. Therefore it is understandable that やっと has a happy feeling attached to it. If I understand English correctly, “at last” has a similar meaning.
とうとう means that something happens as a final outcome, and what happens can be either a good thing or a bad thing.
For example, suppose that some company has been financially in a trouble for a while. Today you heard that the company went bankrupt.
is a usual sentence. If you say
that means that you were waiting for the bankruptcy of the company.
so it seems you are right that yatto is for happier occasions.