Successful breeding of Pets?

Not sure if this helps, but I had issues getting my animals to breed with one another after merging two households, as well as when I tried making them breed with strays. I downloaded the controllable pets mod just to see if there was anything I could do from the animal's pov. With both situations the animals I was trying to breed together didn't know each other. I did the "introduction" interaction with the mod and suddenly they weren't rejecting when I would encourage them to breed. I had tried the "be nice to" interaction, thinking a lack of a relationship was the problem, but they apparently still didn't know each other despite living with each other.

TLDR; If your pets are ignoring your encouragements to breed, download the playable pets mod and introduce them to each other.