Let me copy your statements first:
The core issue, as most scholars agree, is that the two stories were written independently by two authors who never met and had no opportunity to compare notes. Result is a whole series of differences, including this one. For Lk, Jesus did go to Naz. after 14 days - that is not in doubt (Lk 2:39) - they did not return to Bethm but they went from Nazareth to Jerusalem each yr for Passover (Bethm is farther south).
For Matt, they were still in Bethm 1 wk or 2yrs later - time is non-issue. They never went to Nazareth until after some yrs in Egypt, when their …