Yeah, I know. Movies don't have to be accurate in a pedantic way. But I always think it's a bit unfair for filmmakers to trade on the fame of real people and then distort them. Why not just have a fictional magician? In a strange way, it's easier for a role to have reality if it's wholly fictional than if the actor is trying to impersonate a famous person.
Houdini did inordinately love his mother and was heartbroken at her death. But Houdini didn't really take an interest in psychics until about six years after her death, and then he tied his interest into tremendous publicity for himself and for his on-stage exposures of frauds. It was a career move and a sincere crusade. In fact, magicians had been exposing psychics from the stage since the mid-1800s.
His monetary offer was for anyone who could exhibit psychic phenomena that he couldn't duplicate by trickery -- which, you'll notice, is not the same thing as proving that the phenomena was a fraud.
In a separate circumstance, he made pacts with friends that if he could communicate after death, he would use an identifying word known to his wife. It was based on a vaudeville mind-reading code.
In another separate circumstance, Houdini always felt his mother had wanted to say something to him just before she died -- maybe another family member gave him that impression -- but her illness prevented her from speaking, and he was overseas at the time. This was never part of his psychic challenge.
As it happens, Houdini and investigators that he financed did uncover and publicize a lot of crude and lucrative fraud. Houdini had a real hatred for frauds because he knew how cruel it is to take advantage of grief-stricken people. It seems unfair to his reputation for the movie to imply he'd help a fraud.
He and his wife had done a spot of phony stage spiritualism in their starvation years, and he always felt bad about that.
Would Houdini be unfaithful? Not impossible. The most reliable Houdini biographer thought he may have had an affair with Jack London's widow. Houdini's wife, by the way, traveled with him, not his manager. He spent 1926 in North America.