The 28-year-old described the footballer as her "best friend" and a "great dad", insisting that her partnership with dancer Alijaz Skorjanec was purely professional.
"I think it was one of the reservations I had about it really," she said of the tabloid speculation.
"I know what went on and he knows what went on, so it's not like that, you're just learning to dance."
She revealed, "On the launch show I was desperate to be paired with Robin and then when I didn't get him and got Deborah, I was crying my eyes out and got paired with Alijaz."
Asked about her family life with 32-year-old Peter, Abbey said, "He's incredible. He's a better dad than I am mum. I was a bit worried when I got pregnant because he's not used to being around kids, whereas I am.
"He just took to it like a duck to water. He's changed a million nappies, done night feeds, everything. It's amazing to see how much of a great dad he is."
She continued, "I'd love to have more kids. I'm one of four and I've always dreamed of having a huge family. I've loved every second of having Sophia. It's just been the most amazing time of my life. I'd love more of it."
Abbey also said that people's perceptions of her had changed since Strictly. "People see my modelling and see me getting papped all the time, and don't really get to see me because I don't do much TV or whatever.
"I didn't go on the show to prove myself. I went on the show to learn how to dance and have fun, which I did, and on the way people made a different opinion of me."
Abbey also revealed that she chipped her tooth while drunkenly biting the glitterball trophy at the Strictly wrap party.
"My brother's got video evidence with me in the car going, 'Is it real?' Then I woke up and had half a front tooth and was like, 'What the hell?!' It's fixed now!," she said with a smile.