Our parish priest always taught that prayer does not change God’s will for us ....
God has nothing to change, if He did, He would be imperfect.
This is incorrect. Luke 8:43-48 tells us that God willed hemorrhages on a woman for years, and when He, as the Incarnate Word, passed by her, He still had no interest in her healing, per se, but only when she, in faith, reached out to Him did the Messiah heal her. Her very act of reaching out to Him and having faith in Him signaled Our Lord, and He heard her, and He filled her want. If she had not called upon Him, to put a physical effort into touching Christ, He would have still allowed the woman to suffer her illness.
Another event where God changed His will is at the Wedding at Cana. Even Jesus told His mother that it was not yet His time, but she insisted, so He performed His first public miracle before the time He originally set (whenever it would've been) because it still had effected God's glory and it was beneficial to the souls of the people there.
Also, if God does change something, it doesn't mean He made a mistake the first time or He is imperfect. The change He grants will still effect His glory. God will not grant a prayer request if it doesn't effect His glory and it doesn't, ultimately, benefit the soul of the person(s).