The mother of twins who was allegedly struck by a stroller by an American Airlines flight attendant tried fitting the double wide buggy on the narrow plane after being asked to leave it off ... TMZ has learned.

We're told the woman had the stroller tagged by employees at gate check-in and was asked to leave it at the bottom of the jet bridge before boarding the flight so it could be stored underneath the plane.

Our sources say the woman tried to get the double wide stroller inside the narrow plane and employees attempted to remove it. We're told in removing the stroller, the woman was struck while holding her baby ... and nearly ignited a brawl between the employee and another passenger.

American suspended the employee while they investigate and has apologized for the incident, saying, "We are deeply sorry for the pain we have caused this passenger and her family and to any other customers affected by the incident."

The mother and her children were upgraded to first class on a later flight home to Argentina.