I undestand that an alley is actually the opposite: a small, narrow street somewhere on the side. It would translate as 'uliczka' or 'alejka' - similar, but very different.
"Aleja" is a big, wide, representative street, = an avenue.
I think the confusing factor here is English, because in other languages such as German 'Allee' and French (word origin) 'l'allée', it's about the same description as in the Polish one. English, again, is the special kid here.
If we get a sentence for translationwithout any description of the place we may use any translation we choose: alley or avenue/In this case we don`t know where that corner is/
Generally, 'alley' is rather a false friend. An alley is rather narrow, an avenue is wide.
Yes , I think you should stop using aleja for alley and introduce alejka or uliczka