Cynthia Rodriguez will file divorce papers from her estranged husband A-Rod first thing Monday morning in Miami, her lawyer Earle Lilly confirms to Usmagazine.com.

"I'm sure you've heard rumors of the relationship he's had with Madonna - that's the straw that broke the camel's back," Lilly tells Us. "She's been fighting these terrible, demonic problems for two years and they don't go away."

The papers will allege "total emotional abandonment," Lilly explains. "You're not going to see a lot of other relationships named.

"The papers are designed not to be horrible, vitriolic, or create negative feelings, but just to put it out on the table and get this lady through a very troubled period in her life," Lilly adds.

At stake in the split: a pre-nuptial agreement, which is being reviewed by Lilly, the couples' multiple homes and the fortune of a "a baseball player worth close to a billion dollars," he says.

Cynthia, 34, believes that A-Rod's late night visits to Madonna's apartment - first reported by Us Weekly - makes them more than just friends, Lilly says.

"Call it an affair, call it a relationship," Lilly says, "[she's put] up and tolerated his misconduct."

The split, Lilly says, has "been a long time" in the works for A-Rod's wife. The Yankee was was also spotted with a stripper in Toronto, Miami and Dallas in 2007.

"Last year it was published he was with the other woman, and this is the final straw," Lilly tells Us. "She has finally said, 'no mas.' This is what it has come down to.

"Cynthia is a Greek Orthodox lady, brought up in a Greek Orthodox household. She doesn't believe in divorce," Lilly says. "She's devastated, she's hurt, she's a little angry.

"He's a multi-million dollar baseball player, but that doesn't make any difference when there are two little kids at home and no husband," Lilly tells Us.

Lilly says Rodriguez, 32, hasn't seen his daughter Ella - born on April 21 - "more than once over the last several weeks."

(A source confirmed to Us Thursday that A-Rod "literally left 10 minutes after the baby was born, and then was at Madonna's.")

"His activities - despite the fact that he's a very prominent baseball player - don't make him a successful parent or husband," Lilly tells Us.

Cynthia returned to her Miami hometown Saturday afternoon after spending time with rocker pal Lenny Kravitz (who has denied any role in their marriage drama) in Paris.

A-Rod has remained mum on their split, despite reports being released Madonna "brainwashed" him with Kabbalah, a religion the Yankee's father confirmed to Us he's been studying. The New York Post also reported he's "obsessed" with the Material Girl and would "go into a trance" when one of her videos came in at the gym.

Madonna, 49, and Guy Ritchie, 39, went to Kabbalah services in NYC Saturday.

A-Rod and Cynthia have been married since 2002. They are also parents to Natasha, 3.