couldn't this also mean "the child would have an animal?" if so, how does one diferentiate? context?
So I noticed that the other verbs form the past with one word (spiste, talte,etc). Can "have" do that or does it always need ville?
I think here it's more confusion about the main verb. Think of it more like "The child wanted to have an animal" and it might make a bit more sense. "Have" does have (an irregular) simple past tense of "havde" but here, it's ville which is in past tense (also irregular, and the same as its infinitive)