"It's just so hard to find anywhere - and it's even harder if you have animals. At one house we went to, 80 people looked at the house.
"Even if you're an excellent tenant and you're willing to pay good money, if you have animals you're at the end of the list," Ms Rickey said.
Eventually they did find a new rental house - but only because Ms Rickey knew the landlord and talked him into it.
She believes it's unfair for landlords to turn away potential tenants because they have animals.
"If you're a good tenant, you're going to look after your animals well and not let them wreck the place."
Ms Rickey said she would like to see a reference system for animals, with local councils verifying whether a dog was classed as "good", and vets verifying whether both dogs and cats were in good health.
She said pets provided valuable companionship and, in the case of dogs, protection.
"I got Flea when my son was eight. I was a solo mum, so having a dog around was really important for me. Our animals are part of our family."
She said she knew other pet owners who had struggled to find rental accommodation.
Philip Kubiak, Whanganui branch manager for Property Brokers, which manages rental properties, said tenants were "on a second tier" if they owned pets.
I was up to the landlords to decide whether tenants could have pets or not. A landlord might stipulate in a tenancy agreement that a tenant could have only a cat, or a dog only if it is housed outside.
"It would be fair to say that landlords lean towards those who don't have pets," Mr Kubiak said.
He said some landlords allowed pets and charged tenants an extra for them, as they were an "added risk".