In a short video posted on Twitter with the message “Ireland 2022, when a TD can end up homeless”, Ms Wynne discusses seeking to find accommodation in Clare for her family.
The now Independent TD said the number of properties that would suit her situation were “minimal” especially since she needed a four-bedroom house for her family.
A TD is paid €101,193 and because Ms Wynne lives in Clare she is entitled to €31,365 a year in travel and accommodation allowances.
In her video message, Ms Wynne said she had been given a notice to quit and had struggled to find new accommodation for her young family.
“The housing crisis is a major problem in this country and in my county of Clare,” she said.
“I know at the time of the notice to quit, even finding hotel space was extremely difficult and the holiday home was the only answer for our family but it is not a sustainable solution for our family.
“So we remain hopeful and hopefully we do get good news,” she added.
She did not respond to requests for comment on the video.
Ms Wynn resigned from Sinn Féin in February claiming she had been “isolated” and subjected to “psychological warfare”.
The Clare TD, who is on maternity leave after recently giving birth to her sixth child, said she did not feel supported by the party after her election to the Dáil in 2020.
She also claimed her “unplanned pregnancy” was used by some in the party as a “stick to beat her with”.
Ms Wynne said she was disappointed that Sinn Féin leader Mary Lou McDonald had not contacted her to congratulate her on the birth of her most recent child.
However, she did receive a handwritten note from Fine Gael leader Leo Varadkar.
Ms McDonald sent the former TD a card and gift after Ms Wynne publicly complained about the lack of acknowledgement from the Sinn Féin leader.