What do you think of exes who share animals?

I have an ex of several years, and we have a dog together. We each take her every other week. I was the one who broke it off, and I couldn’t take her away from him too after I broke his heart. It’s very inconvenient, and I know it prolly hinders him from completely moving on. We’ve been doing this for like 10 months. I am the one who takes her to the vet, trims her nails, takes her back and forth, gives her medicine, etc. I onlty do this because I really love my dog, I am in a new relationship that is great for me, and I don’t know how to go about ending this weird custody thing, because I know it will be a huge fight and I don’t want to fight anymore. Anyone out there who has done this/is doing this? Advice please!