Rini never has Чиби Chibi. Чиби Чиби is not Rini's daughter because Чиби Чиби isn't even a real person.
Here's what wikipedia says "In the manga, Chibichibi's childlike form is really a disguise for Sailor Cosmos, an ultimately-powerful Senshi from the future." (She is Sailor Moon's ultimate form in the future) "In the anime, Chibichibi is the starseed of Sailor Galaxia, who had once been a great force for good."
So Чиби Чиби isn't even her own person. In the manga, Чиби Чиби is actually Sailor Moon in disguise. And in the anime, she's just a crystal that belongs to someone else.
In the manga, I think Rini becomes Sailor Mini Moon at the end of Sailor Moon R, in Act 23. In the anime, she becomes Sailor Mini Moon in Sailor Moon S, in episode 103 (Japanese sub). (or in the English dub, episode 96)