Mr Mullan and his children were eventually placed in temporary accommodation in Belfast in October 2023.
The family temporary accommodation service currently houses 27 adults and 42 children.
"I am very fortunate to be here," he said.
"Having my own cooking facilities felt like I'd won the lottery. I felt like I had a burst of life again."
However, he said the pressure of being homeless has had a significant effect on his two children.
"My daughter in the mornings doesn't want to get up out of bed," he said.
"She is feeling frustrated and she doesn't have that healthy way to get her feelings out.
"It's very confusing for them. You can't set up her room for her.
"If she wants unicorns you can't decorate. It feels like you're living in a blank space. You still feel like a guest."