I am sure that this is an easy one for the vets, but I am not sure on rule.

B2 is unreported sub batter. R1 on 1B. B2 becomes B/R by hitting safely and reaching 1B. R1 goes to 2B on the play. Coach of defensive team brings unreported batter to attention of ump. First time is warning only to the team and the play stands--right? If it happens a second time, unreported batter who reached 1B safely is out and all runners return to base--right? If this is correct, do base runners return to base occupied at time unreported sub batter entered batter's box or do they return to base occupied at time unreported sub batter reaches base?

Depends on which set of rules you're using. In NFHS, as long as the unreported sub had entry/re-entry rights in this slot of the batting order, the play is legal. You would issue a team warning to the offending team and play on. The next violation by that team would result in the player being restricted to the bench.
In NSA Fastpitch, an unreported sub is treated like an illegal player and is handled like a protest. In your scenario, the unreported sub would be declared out. Both the sub and her coach are ejected and any advances made by other runners as the result of play by the illegal player are nullified. Not sure about ASA but there are lots of ASA umps that can help.

In ASA, the unreported sub is

a) fixed without penalty if discovered by the offending team, all previous play stands.

b) handled as a protest by the offended team. The unreported sub is DQed and removed from base/field and replaced with an eligible sub. All previous play stands. No out is charged unless the team goes shorthanded. Then the shortanded rule is applied to determine if an out is charged.

Sorry, I was asking for NF but also need for ASA. So in NF, second time it happens, unreported sub is removed from game and restricted to dugout. If that unreported sub is on base, then what? Does original player or other sub take her place on the base. If original player takes her place on base, is that a re-entry?