She also claims that Mr Queally, who she has not seen for months, had been living a double life and had another fiancee while engaged to her.
Yesterday at the High Court Queally's lawyers said claims he had transferred money from a joint bank in the US to his bank account in Ireland without Ms Rodino's authorisation were simply untrue.
The court also heard that Mr Queally rejects her claims that Ms Rodino was his fiancee or that he was engaged to another woman in New York.
Last month Ms Rodino's lawyers secured a number of temporary freezing orders against Mr Queally, of Sherman Avenue, Yonkers, New York, who is originally from Lahaknock, Kilmaley, Co Clare.
They prevent him reducing, dissipating or transferring funds below a value of €1.6m held in a bank account at Permanent TSB in Ennis, Co Clare.
Ms Rodino, of Cathedral Avenue, Hempstead, New York, claims the money in the Ennis bank account, approximately $2m (€1.5m), is hers. She claims that it was moved by Mr Queally from a joint account held in the US in both their names.
Yesterday, Patricia Hill, for Mr Queally, said her client rejected all the allegations.
Counsel said it was Mr Queally's case that on October 18 last Ms Rodino had signed a document at a New York Bank that stated that any funds transferred from a joint bank account to Mr Queally's bank account was done with her full permission and authority.
This document was executed in the presence of a notary presence, counsel said.
On that basis, counsel said it was intended to ask the court to vacate the freezing order on the ground there had not been a full and frank disclosure of all material facts to the court.
Counsel also told the court that Mr Queally rejected claims that his two teenage children from his previous marriage had been put through a private Catholic schools in New York with money allegedly taken from Ms Rodino.
Mr Queally's children had been attending private schools from a very early age and many years before he and Ms Rodino first met.
In reply, Ross Gorman, for Ms Rodino, said that any application to set aside the freezing orders would be opposed.
Ms Justice Iseult O'Malley agreed to adjourn the matter to early next week to allow Ms Rodino's lawyers reply to Mr Queally's affidavit.