First find out if the alternator is defective.

Second find out if there is a load on the alternator
when the car is stopped and closed up (that is,
when it is closed up for the night). You would need
to measure the current through the battery for this.

Third have the battery checked to see if it is ok.

I wouldn't think that replacing the alternator
is going to help you any if the battery is bad or
there is a load that shouldn't be there on the
battery.

I would think that replacing the alternator with any
working alternator would fix the problem if the alternator
is bad, and I would think that replacing it with the OEM
would be best.

I do not see that replacing the alternator with a bigger one
would help except in some bizarre circumstances. Namely
if you are using more than the current alternator would provide when driving around or if you are discharging your battery
during the night and then only driving it a short way during the day.

I must admit I've only read your original email only once and might have missed something.