This is a mix of two constructs that might be a bit hard to get for learners of the language - A construct using dative to express "I accept" (maybe close to the English "Fits/suits me"), and the whole thing in subjunctive.
Aunt Petunia said "It won't ever enter the house"
Tante Petunia sagte, "Das kommt mir nicht ins Haus"
(So basically an expression of "I will not accept it", or "I can't have that happening", which can be expressed by a dative in german like "mir...nicht"). A good example is the (colloquial) saying
Das kommt mir nicht in die Tüte
which roughly translates to
I don't accept that
Now put the whole sentence into subjunctive:
Aunt Petunia wouldn't have accepted it entering the house
Or in German, simpler:
Mir kommt es nicht ins Haus
And, then re-formed to
Tante Petunia wäre es nicht ins Haus gekommen
That special dative construct is seldom used other than in first person, i.e without "mir", so it is even uncommon in German.