"Tini has these books at home."
Translation:Tini punya buku-buku ini di rumah.
As a native speaker, I would say "ada" cannot replace the verb "to have". "Ada" means "there is" or "there are". You can use "punya" or "milik" to say "to have" or "to possess".
My Indonesian son in-law says it all varies bepending on the context but this is basically how it goes
ada= there is or It is ada di = it is in di =in
Tini punya buku buku ini ada di rumah. was wrong. apparently you have to drop the ada. WHY???
As a native speaker, I would say the sentence is wrong. And yup, you need to drop the "ada" (= there is/ there are), because it is not needed and is confusing.
In English, your sentence will be translated as "Tini has these books there are at home." Guess what is wrong with the sentence? The "ada"!
According to the Echols and Shadily dictionary the official meaning for ada are, 1 there is, are e.g. Ada anjing di sini. There is a dog here. 2 be, be present e.g. Saya ada di New York. I am in New York. 3 have, own e.g: Dia ada mobil baru. He has a new car. Also confirmed by Indonesian friends. I'll leave it at that.