This is not a get-even exercise by a daughter against a famous mother. Although as Parker spins her life story with élan she expresses her repeatedly dashed hopes for a loving mother-daughter relationship, she respects MacLaine for what she has achieved and in addition to the complaints, she talks of the fun times she has also had with her mom. But she is unsparing in her amusing, and sometimes sad, accounts of MacLaine’s idiosyncracies. Much is downright funny. She is very skillful at delightfully imitating her mother in pungent conversations that she recalls.

Parker becomes an exceedingly enjoyable companion. She is likable, mainly because she is effervescent and outgoing, and also because she kids herself as well as her mom and her late problematical father. She is a resourceful actress, with excellent timing, and she knows how to veer between comedy and poignancy. It is an amazing journey that she takes us on, from her being sent to live with her father, Steve Parker, in Japan, with the excuse that she was in danger of being kidnapped by “the mob,” through her having a family of her own and having come to terms with who she is and achieving an independent life.

She describes growing up in Japan, with her father having a mistress, whom he abused, to her Japanese governess, stern but affectionate. She can be a funny mime, as when she describes the seven layers of brown underwear she was required to wear, and going to the side of the stage to demonstrate hilariously how when she had to pee, she had to slip down one layer at a time, and then pull up one layer at a time.

At times she felt she was daddy’s little girl, at other times she felt abandoned. She looked forward to visits with her mom in California, but, as she describes it, the fun occasions were marred by a feeling that her mom’s attitude toward her was basically perfunctory without the demonstration of the love that she craved. During her childhood there was the glamour of Hollywood sets and the celebrity crowd, but never the motherly approval she sought. She describes her mother’s frowning on her ability when viewing her in a movie role, and her mother encouraging her to concentrate on cooking instead of on acting. One gets the impression that MacLaine only wanted one star in her family.

When Parker finished the schools she attended and expected to go to college, she recalls, her mother frowned on the idea and urged her to go out and make her way in the world as she had done. That she did, with a variety of jobs and a period of fun promiscuity. Eventually, she moved into acting, but not until her mother saw her act later in life in a production in Connecticut did she tell her how good she was.

A major part of the play is devoted to satirizing her mother’s re-incarnation beliefs, such as once having dated Charlemagne and then dating the person Charlemagne came back as. (I recall Johnny Carson once joking on TV that it was a good thing he had never been married to Shirley MacLaine, or he would be paying alimony all the way back to ancient Egypt.) But the situation gets more serious than the reincarnation kick.

Parker tells how her mother once showed her a box full of telegrams of messages that were coming from Sachi’s “real father” in outer space. MacLaine said the Steve Parker in Japan was really a clone of her real father, set up secretly by the government for security reasons to cover the work of her real father in space, and that she was supporting the program with $60,000 a month sent to the clone in Japan. In the show, Parker recalls confronting her father on his death bed, and he admits that he had duped MacLaine all the years with the fake telegrams and getting the money that he used to support his extravagant lifestyle. It is the wackiest tale of all in “Lucky Me.”

Although the play gets a bit soppy at the end with Parker’s life affirming conclusions, she does leave one with the feeling that all came together happily for her once she stopped seeking motherly approval and stood as her own person, enjoying motherhood and lavishing the love on her own daughter that had eluded her. Above all, she achieves the audience appeal she might not have had if she were vengeful toward MacLaine instead of able to look with amusement and maturity at her mother in defining the kind of personality the star became in the light of her considerable achievements. Curiously, she never mentions her uncle, Warren Beatty.