Since domestic animals wouldn’t exist had we not brought them into existence don’t we have a right to use them?

No, even though we may have some responsibility for the animals that we have brought into existence that does not mean we have the right to use them as a resource.

If we used that reasoning then our children could be used as resources also. Although we have some authority over how are children are treated, there are limits. For instance we can’t enslave, kill them or sell their organs. We have as a cultural norm a moral obligation as parents to care for our children and not exploit them. So too do we have an obligation to look after animals that we have brought into existence, however the question that must be asked is whether we should be bringing them into existence in the first place.