The Worrisome Witness

D is accused of murdering V on June 1 between the hours of 9 and 11 p.m. at V's home. The alleged motive is revenge for V's ending their longtime business relationship. At trial V's maid, Emma, gives scream-scram testimony for the prosecution: She heard V scream, she saw D scram. The defense is an alibi. The principal defense witness is W,who testifies that from 9 to 11 p.m. on June 1 she and D were at the office working together. In rebuttal the prosecution offers to prove through C, a cashier at Martin's Liquor Store, that on May 1 he saw W steal a case of Remy Martin by pretending it had been paid for when in fact it had not. D objects. What ruling and why?

Suppose that the prosecution offers to prove on cross-examination W's conviction for grand larceny for a theft of a case of Remy Martin from Martin's and D objects. What ruling and why? What reasons are there to treat the two situations differently? If the prosecution introduces evidence of W's prior conviction, should the defense in surrebuttal be allowed to elicit from W testimony that she was convicted but was framed and is really innocent?