Is your 16 mo old in a big bed or still in the crib? I ask because I think you and dh should sit down together with your 3 yo dd and tell her that babies do not go to bed on time and babies wake up in the middle of the night and won't go back to sleep because they don't know any better. You and dh thought she was past that stage but since she has shown that she is not, you will need to put her back in the crib until she can have better night time habits. Then I would show her a chart that you have made in advance. Tell her if she gets so many stars on her 'bedtime and sleep through the night' chart (you and dh determine how many is enough), she can have her big girl bed back.
I would definitely not let her sleep with you or with her sibling because I think you are allowing her to manipulate the family into changing the rest of your sleeping habits to accommodate her. (You don't want your younger child to develop bad habits either.) This may end up encouraging her to manipulate in other areas and once this kind of behavior starts, it's tough to put a stop to it.
As far as her bedtime goes, pick a time that you and dh agree is reasonable, say 8:30. Write down what your routine is going to be and stick to it every single day. Routine at bedtime, like at other times of the day is a key for your child to learn to develop good habits. The night time routine needs to be soothing and relaxing, something your child can look forward to. Baths and story time are great for this time of day. Hope this helps, S.