"Can" you sue? There is an old saying, "you can sue a ham sandwich." The real question is whether you would have much chance of winning a lawsuit for libel against the father's attorney. There are few absolutes in life, but I would say you have almost no hope of winning such a suit.
Even on a level playing field, you would not convince a jury that, most likely, the lawyer knew the letter to the psychologist was false or acted with actual malice. In all likelihood the lawyer did not invent these accusations out of thin air and has no malice against you apart from aggressively representing the father. She based her letter on what her client claimed to be true.
The law of libel, slander and defamation is NOT a level playing field. Such suits are discouraged by the law. "If the alleged defamatory statement is made to achieve the objects of the litigation, the absolute privilege applies even though the statement is made outside the courtroom and no function of the court or its officers is involved." Romero v. Prince, 85 N.M. 474, 477, 513 P.2d 717, 720 (Ct. App. 1973); Penny v. Sherman, 101 N.M. 517, 520, 684 P.2d 1182, 1185 (Ct. App. 1984) (noting that statements made in relation to “an ongoing or contemplated judicial proceeding” could receive absolute privilege protection); but see Gregory Rockhouse Ranch, L.L.C. v. Glenn’s Water Well Serv., Inc., 2008-NMCA-101, ¶ 19, 191 P.3d 548, 554 (denying absolute privilege defense as to particular communications because they were made at a time well before litigation was seriously contemplated). Because you're "involved in a child custody case" and the letter was made in relation to that case to achieve a better custody decision, the absolute privilege will result in the new judge in the defamation suit summarily throwing out your lawsuit.
Rather than waste precious time and money in an ill fated lawsuit against the lawyer, you need to convince the psychologist that these accusations - originating as they must from the father - are not true. Even as a fit mother, as you will no doubt be found, the court will still favor an arrangement where the father has reasonable visitation rights - after all, it is "his" baby too.
It would be an uphill battle.
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