The actor, 48, presented the request to Los Angeles' Superior Court on Friday, after Alice, 53, filed for sole custody of Elsie, eight, and Ella, 12.
Ioan alleged in court documents, obtained by MailOnline, Alice verbally abused him throughout their 14-year marriage and shared his heartache that he hasn't seen his eldest daughter since last July.
He reportedly claimed: "Since I moved out of the family residence in January 2021, Alice has inflicted serious emotional harm on Ella and Elsie by her statements and by interfering in my relationship with them.
"Alice has verbally abused me in front of the girls throughout their lives".
The Fantastic Four star went on to claim Alice would mock his appearance often, making quips about his hair loss and "telling me I had 'saggy-vagina eyes'."
Ioan also slammed Alice's "false social media narrative" that she was blindsided by the divorce and he abandoned the girls.
He alleged in the court documents: "To this day, Alice continues to post false and misleading statements about me on social media. Alice has stated repeatedly that I want nothing to do with the girls, I refused to see them and I abandoned them.
"Alice posted she fears she and the children would starve and become homeless because I refuse to contribute to their financial support.
"None of this is true and I fear that Alice's false social media narrative is constantly being seen by the girls, and repeated to them by Alice."
Ioan went on to ask the judge for his daughters to attend therapy over worries the impact of their bitter split is having on their children.
Mirror Online has contacted Alice's representatives for comment.
The actor filed a restraining order against the 102 Dalmatians actress back in February.
He requested Alice, 53, should have to stay 100 yards away from himself and his girlfriend Bianca Wallace, and that she should not be able to contact them.
In the court documents signed on Tuesday 14 February 2022, Alice has rejected all of Ioan's claims and accused Ioan of filing the request as "a ploy to gain some sort of advantage" over her in the upcoming divorce proceedings.
Ioan ended his 21-year relationship with Alice in January 2021.
He filed for divorce in March 2021 following 13 years of marriage. Seven months later he started a romance with Australian actress Bianca, 30.
Alice has accused the couple of conducting a three-year affair - an allegation they have both vehemently denied.