Hall, 38, shared a quote on Instagram from author Jonathan Muncy Storm that seemingly alluded to Anstead's ex parte application, which a California Superior Court judge in Orange County denied because Anstead, 43, failed to prove there were critical circumstances concerning the child.
"She will test you and see what you're made of, just by being herself. Because the nature of a strong woman will identify who a man really is. If he feels threatened or has the need to possessively control her, it will be revealed. And the funny thing is that she doesn't want to call the shots. She wants a man who will embrace her strength and stand by her side. A man who will walk with her but will lead with taking the first step," the quote reads.
In the caption of her post, Hall shared a quote from a different author, Jill Blakeway: "When a toxic person can no longer control you, they will try to control how others see you. The misinformation will feel unfair, but you stay above it, trusting that other people will eventually see the truth just like you did."
In a response filing from Hall and her legal team, obtained by PEOPLE, she says she was "shocked to see the false allegations against me and [Anstead's] belief that he has been failing to protect our son by sharing custodial time with me."
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"Mr. Anstead has now taken the position that he is the defacto primary parent of our son, which is not accurate. Anstead does not count any day wherein we exchange our son as a custodial day for me. He also counts days where I made an accommodation or gave a right of first refusal to him as his day," says Hall.
"That is why there is a huge discrepancy in his mind from our accurate schedule. His attempt to mislead the court is transparent when presented with the true facts."
In response to the filing on Thursday, Hall told PEOPLE exclusively, "What Ant is doing deeply saddens me. If this was really about Hudson, as he says, this should have been handled privately with a private judge or mediation, as myself and my attorney have suggested."
"I have had my share of ups and downs but I am a good mom and I love my children with all my heart and I will always protect them," she adds.
Following the judge's ruling on Thursday denying the ex parte application, a hearing has been set for June 28 to allow both parties to appear and make their arguments as to whether the requested change to the custody should be granted.
A rep for Anstead had no comment.
Michael Kovac/Getty; Allen Berezovsky/Getty
Anstead and the Christina on the Coast star were both granted joint legal and physical custody of their son after their divorce last July.
In December 2018, the former couple wed during a surprise ceremony at their home in Newport Beach, California. They welcomed their son in September 2019, but a year later, Hall announced the pair had split in a statement posted on her Instagram.
"We are grateful for each other and as always, our children will remain our priority," she said in September 2020.
Hall shares son Brayden James, 6, and daughter Taylor Reese, 11, with ex-husband and Flip or Flop costar Tarek El Moussa. Anstead is dad to daughter Amelie, 18, and son Archie, 15, from his previous marriage to Louise Storey.
The former pair have both moved on as Hall recently married realtor Josh Hall, 41, after a year of dating, while Anstead has been in a relationship with Renee Zellweger, 53, since last June.