The prevailing wisdom for most umpire manuals in a crew of three is that check (or "checked" in softball parlance) swings for lefties get appealed to U3 and righties get appealed to U1. That's what most umpire manuals will tell you, such as a prior year's NCAA Softball Umpire Manual, which states, "The plate umpire should get help from the first base umpire for right-handed batters and the third base umpire for left-handed batters, regardless of where the base umpires are positioned on the field."
Professional baseball, at some levels, did experiment years ago with having the third base umpire take check swings on right-handed batters during situations in which the first base umpire is counter-rotated onto the infield, such as the runners on 1B & 2B situation in LSU-Louisiana...but the experiment didn't seem to work and umpire mechanics returned to the U1/righties and U3/lefties setup.
Looks like softball is angling for a new check swing mechanic experiment.
Video as follows:
Alternate Link: Who takes a RHH check swing appeal: U3 on the line or U1 on the infield?
Video as follows:
Alternate Link: Who takes a RHH check swing appeal: U3 on the line or U1 on the infield?
