I understand the landlord's point of view.
When my BF and I were looking for an apartment to live together, it was hard because we had Nena.
We found a nice place (where we live now). The apartment is big enough for us and the rent is good and the neighborhood is awesome.
The only problem the landlord had was that we had a dog.
They've had bad experience with previous tenants and pets and that's why they didn't want tenants with pets anymore.
After discussing with them an telling them how Nena behaves etc. They decided to let us in and gave us a proof period of 6 months. Within those 6 months they came to visit and to see how the house was and how Nena was and they liked that everything was ok and well taken care for that they gave us a 1 year contract.
When we decided to add Rufus to the family, we told them about our plans and they agreed with us