"I am not willing to comment in public on the custody discussions regarding my children," Gosselin says in a new statement. "What I will say is this: I am and always will be a mother first, but as a single working mom, I will do everything necessary to provide for my kids despite the opinions of others."
Jon's lawyer tells PEOPLE that Kate is an "absentee parent," citing her current stint on Dancing with the Stars which shoots in Los Angeles. "He wants equal say with custody, equal time, but if the circumstances remain as they are, with Kate being rarely home, Jon wants primary custody of the children," says Anthony List Sr.
Meanwhile, Kate's lawyer Mark Momjian tells PEOPLE he has not received a formal filing yet but that "our client is a devoted mother who loves her children very much."
Kate, 35, is about to start a publicity campaign for her new book, I Just Want You To Know: Letters to My Kids on Love, Faith and Family, which is set to be released on April 13.