Runner at 3rd is going on contact, if he is clearly beaten by throw he should stop and get in a run down to allow batter time to advance to 2nd. Batter needs to anticipate this if throw is made home.
We run this play many times per season, over a period of many years.
The "R3 rundown/batter-runner advances to second"scenario you describe is infrequent to the degree that I'm not going to clutter my batter's brain about it during his at-bat.
Our 1b coach is very aware of this scenario. It's his job to anticipate it...that same way that it's my job (as 3b coach) in this scenario to anticipate having two runners standing on third base.
Also, IME, batter-runner advancing to second base (while R3 is in a rundown) is NOT a gimme, and often is NOT an easy read for batter-runner/1B coach. Keep in mind, we run the r2/r3 contact play regardless of the speed or IQ of R3, which means that their ability to prolong a rundown (to allow B-R to gain second) is not necessarily top notch (understatement).
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