I can understand why that would make you feel shocked and ill. Just the implication of such a thing is enough to do that. Is your father usually very honest without considering how things might come across or the impression he might give of himself?
I would strongly advise against seeing a therapist to try to recover possible repressed memories of child abuse. There has been much media coverage of people, particularly women, who did this and the therapist recovered false memories. This resulted in people being wrongly accused of child abuse and imprisoned, and has broken up many families.
"The trauma-memory argument and recovered-memory therapy have been with us for more than 100 years, and have embedded themselves deeply into both our professional practices and our wider culture. But there was never any good evidence for either, and there still is none. Maybe such evidence will be forthcoming in the future. There are occasional cases in which traumatic stress and amnesia seem to go together, inviting interpretations in terms of repression or dissociation. But nothing in the case literature justifies assertions that trauma impairs memory as a matter of course, or in the majority of cases or often � even sometimes seems too extreme. In view of the paucity of evidence that trauma causes amnesia, discussion of implicit memories of trauma seems pointless. Laboratory analogs of traumatic amnesia are models in search of a phenomenon; theories of traumatic amnesia are explanations in search of facts."
Before making any decisions, it's a good idea to investigate evidence such as that presented above so you can make an informed decision.
I think it's quite plausible that your mother made untrue accusations. When my parents divorced, nastily, when I was 13, they were both badly hurt, and seemed to turn from "normal," loving parents into nasty, vindictive people who cared more about hurting each other than they did about their child. Divorce brings out the worst in people, sorry.