I don't think there is much wrong with this. The child has been through so much with an addicted parent, meth is a horrible addiction, she probably has been neglected, and needs extra tlc. If you get married then you have a say, but since you are not, he's probably getting annoying because truly it is not your family, or your business. He needs to focus on her, and feels it is in her best interest, not your feelings about it.
In a lot of other cultures this is acceptable until the child reaches puberty.
Don't mean to be harsh, maybe you should take a step back and let this issue go for now.