The Celebrity Big Brother winner explained that she is having some "time apart" from her fiancé while he does filming work in Wales, which she hopes will strengthen their relationship after he temporarily moved out of their home.
"I think having time apart is a good thing, especially as things have been strained between us," Houghton wrote in her New column.
"Another magazine said he and I are heading for a custody battle over Dolly, but that's not even on the agenda. We haven't split up."
Houghton also denied suggestions that she now hates Reid following their fight about his "sexual preferences".
"Of course I was upset, anyone would be in my position, but I don't hate him," she said. "Hate is a very strong word."
The couple have faced a number of relationship issues both before and after the birth of Dolly on June 17.