If your names are Hakka, and not mandarin, then I can't really help you, because those are two different languages/dialects.
If Osmanthus fragrans is correct, then the chinese characters for your name would be : 桂花 (pronounced "gui hua" in mandarin), literally "cinnamon flower" or "cassia flower"
Since you and your sisters all have the same "Kwai", your names might all be based on the same flower-type: 桂 (osmanthus, laurel)
So it might be a lead to find words starting with this character and then check their Hakka pronunciation?
btw, I don't think the spellings of your names are incorrect, but rather there is no "correct" one. It's just a try of expressing a certain pronunciation in our alphabet and I suppose there is nothing like "pinyin" for Hakka.
My guesses for now are:
Kwai Lin: 桂蓮 ("laurel/osmanthus" and "lotus") or 桂林 ("laurel/osmanthus" and "wood, timber")
Kwai Larn/Kwai Lan: 桂蘭 ("laurel/osmanthus and orchid")
Kwai seems to be frequently spelt as "Gwai" as well. I was able to find at least a few people on the net bearing those names (character combinations).
But well, this might be completely wrong as well, but at least it corresponds to the "flower names"-hint =)