The difference between these two forms exists in English or other languages, too. Basically, a lot of verbs have a ‘person they affect’ which can be somebody else (non-reflexive) or oneself (reflexive). I tend to usually ignore that two forms of these verbs exist and just remember the non-reflexive one since it is more general.
Thus, I would suggest you remember the verb as:
jemandem etwas{akk} wünschen
With the additional information that jemandem can also be oneself, i.e. sich{dat}.
I’m not sure if verbs with two dative objects exist, but if they do they are rare. Thus, having a dative mich alongside a dative object euch should set off alarms. The only correct form is:
Ich wünsche euch einen schönen Abend.
If you want to wish yourself a nice evening you might say:
Ich wünsche mir einen schönen Abend.
But in this case only you are the recipient of the wish; nobody else can be. (Okay, they could, but that would be mir und euch.)