The actor, 48, filed the request in in Los Angeles Superior Court on Friday last week - months after Alice, 53, filed for sole custody of daughters Elsie, eight, and Ella, 12.
In the filing, Ioan recalled details of his 14-year marriage with the 102 Dalmatians actress, alleging that Alice had been verbally abusive.
Detailing his version of events, he went on to claim she "undermined [him] in front of the girls throughout their lives" - including poking fun at his appearance.
"Alice made fun of my appearance often, making hair-loss comments and telling me I had 'saggy-vagina eyes,'" the court papers read.
Titanic star 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."
The actor is adamant Alice has been purposely trying to cut communication between himself and their children since their bitter split.
The Mirror has contacted representatives for Alice and Ioan for comment.
Back in February, Ioan took out a temporary restraining order against his former wife.
He requested Alice 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 court documents signed on Tuesday 14 February 2022, Alice 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's lawyer is now seeking a continuation of a restraining order against Alice.
Ioan ended his 14-year marriage with Alice in January 2021.
He filed for divorce in March 2021, before moving on with Australian actress Bianca, 30, just seven months later.
Alice has accused the couple of conducting a three-year affair - an allegation they have both vehemently denied.
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