Sims need to develop a relation before the may have sex.
Makes sense in most cases and you may mod it out using ACR or items such as the Easy Bed, etc.

Do you know any similar mod or item for pets?
I would not mind if it removes the friends-with-owner check or not, but I would like my pets to be able to breed in a more instictive manner.
So.
A mod that allows them to breed autonomously, no matter the relation with other pets?
Or a modded pet house maybe?

I would like that too, or a mod that allows relatives to breed. Line breeding is a common way in REAL life to improve breeds, and it's not "nasty" for them to breed like that.

It is a bit creepy that my RL dog's father is also her grandfather. XD

Sounds like a song . . . https://www.youtube.com/watch?v=rXU-ZdmzNmo

I had some kittens with that issue. Who also didn't know who was a sibling and who was a cousin. Not that they weren't all half siblings due to the father issue, but... The story if you want to know, is that my male (A) and female (B) had kittens, of which only two of the litter (C and D) survived. Both were girls and both were later impregnated by their father. And had their litters within hours of each other. So all the babies were all grouped together (by the mothers, I nor any of my family had anything to do with it. We were prepared to let each mom have her own space) and the moms took turns on kitten watching duty. Those babies had a mom with them at all times for a while. And now that I've completely derailed the topic, I'm going to go. After I say that I want this mod too. One of my sim dogs is completely refusing to have puppies with either of the two females on his lot, despite everyone having great relationships with one another. I'm about to roll a die and impregnate of the the females with the Sim Blender... ~VP