"This is your child."
Translation:Это твой ребёнок.
Твоя is for female like моя мама everything ending with я. Твой is for Male 0
Maybe with the word "child", the automatic classification is male if the gender is not known. It would be stange with the fact that all unknown-gendered cats are female until proven otherwise.
твой / твоя are informal "your" and ваш / ваша are formal "your" (similar concepts in French and German)
why is это ребёнок твой wrong? is always thought that the ordering does not really matter.
Though the ordering doesn't effect the sentence grammatically, in this case, the ordering you're suggesting sounds a bit... too "poetical". Usually, the noun should follow the related pronoun.