Question is on catch and carry on out of play line.
Runner on second, 1 out, ball hit to out of play line by first base, first baseman makes a catch, either with both feet in play steps out with one foot, pivots and comes back into play. Ruling? Or he is straddeling the out of play line, and pivots back into play after the catch. Ruling? In both cases his one foot always was in play. The initial ruling was the plate umpire said no catch and gave the runner at second 2 bases to score the winning run. Then changed his mind, ruled a catch, and gave the runner at second third. Is this right?

It depends on which rule book your league plays with. Under NFHS (high school) rules, the player has to catch the ball with at least part of each foot in play for a valid catch. Then if he steps over the line accidentally, all runners receive one base. In Official Baseball Rules (rules used for almost everything else like American Legion, Pony, and LIttle League with some small modifications) the player still must catch the ball while in play, but if he runs out of play the ball remains live. If he falls out of play, then each runner receives one base.

rule reference under nfhs, I see the table in rule 8.3, but must be missing the reference to it. thanks for your help

Wrong answer for NFHS !
 

One foot out is a live ball. Both feet must leave the field of play before the ball becomes dead.

NFHS 5-1-1i
Ball becomes dead immediately when: a fielder, after catching a fair or foul ball (fly or line drive), leaves the field of play by stepping with both feet or by falling into a bench, dugout, stand, bleacher or over any boundary or barrier such as a fence, rope, chalkline or pre-game determined imaginary boundary line.

NFHS 8-3-3d
Each runner is awarded: one base if ... or with less than two outs, the batter his a fair or goul ball (fly or line drive) which is caught by a fielder, who then leaves the field of play by stepping with both feet or by falling ...

OBR 5.10f
The ball becomes dead when ... a fielder, after catching a fly ball falls into a bench... FEET NOT AN ISSUE.

I'm sure glad someone pointed that out to me at the end of the season;-)

End of season? The only months I don't have games are January, November and December.

End of high school season. No summer leagues use NF rules in my area.

You did not specify. In my area there are many playing Fed rules year-round, AAU ball for example is nearly Fed rules.