Can you use two that's in a sentence?
You mean, right next to each other, like in this sentence: "They had to remind her that that is not allowed."
Yes, you can. It definitely sounds awkward, and most professional writers will try to avoid it whenever possible. But I don't think it is considered to be grammatically or stylistically incorrect.
Same goes for other words, like "is": "It's not dangerous, and anyone who says it is is simply misinformed" or "They had had no food or water since the day before yesterday."