D.W.
Because she is potty trained during the day, I would probably investigate Antsy Pants first. They get great reviews, come in cool colors. They are cloth but designed to go on like a pull up. You can also adjust the absorbency by using things like large hemp liners along with a microfiber insert. I believe they have a nighttime package that you can buy. Don't be shocked by the price. You will get lots of use out of them and can use them if you have another child or you can sell them once you are done. Just make sure to care for them properly and you will get someof your money back!
You could also look into a pocket diaper that you can adjust the absorbency. What brand will depend on her height/weight. Fuzi Bunz makes a larger diaper as does Thirsties.
Wetting the bed at 3 is perfectly normal. Day and night are two completely different worlds in potty training land. Could take up to age 5 or 6 and that's normal.