Ok so the basis of my question is I am planning on playing a multiclassed character of the above combo.  As a sorcerer I took the cantrips booming blade and green flame blade.  These cantrips read that you cast them as part of an attack action.  My smite spells as a paladin (such as wrathful smite) are bonus action spells. A I understand it if you cast a bonus action spell you can still cast a cantrip on your turn with your action.  So is it reasonable to understand that I can attack with a sword attack empowered by both wrathful smite, and green flame blade?

Yup.

The spell isn't cast as part of an attack action, a melee attack happens as part of the cast a spell action. That is important because if you ever get the paladin side to 5th level, you cannot do this and get 2 attacks per round. But with that said, what you are trying to do is possible. 

If you really want to stack things up, you should notice that Wrathful Smite is a concentration spell that lasts for a minute. You can precast it within a minute of your intended attack and still benefit from it, leaving your Bonus Action free to do something else like a quickened spell, as long as it's not another concentration spell.