With the popularity of Frozen, it was almost a given that the movie would get a follow up. Before they could release one, however, Disney gave rights to the ABC show Once Upon a Time to use the characters in an arc through the first part of Season 4. They used most of the characters from the movie, and came up with a very unique storyline, starting from a short time after the events of the first film took place. While some may be straying too far from the source, such as the Snow Queen, some of the ideas could be very useful in the follow up to the 2013 film.
1. Hans and his brothers
Hans has mentioned before that he is the youngest in his family, and part of his anger and need for power seems to come from that. With so many brothers, he really doesn't have any say of his own kingdom, where there is a long line of succession to the throne. In the show, he and a few of his brothers are back to get revenge. They tease him and obviously think very little of him, and it would be interesting to see him try to get his revenge and earn his siblings' respect finally in a more driven way then something that seemed tacked on as an afterthought.
2. No singing
Being a Disney film, this seems unavoidable. However, even on the show they pick a little fun at it. I think many of us would rather not have another 2 years of "Let it Go" sung ad nauseum everywhere we go.
3. Kristoff and Elsa's friendship
With Kristoff having such a good sense of humor and Elsa needing a little lightening up, she needs a friend like Kristoff that can tease her and be there for her, even when Anna can't be around. Her queenly manner and his working man attitude would be fun to play with, and could be funny to see on the big screen
4. Anna and Kristoff's marriage
I am not saying that that should be the focal point of the movie, but similar to the way it was done on the show, Frozen 2 could end with this celebration after the defeat of Hans and his brothers. Setting the movie maybe a year or two after the original events would mean that they had actually dated and gotten to know each other so there wouldn't be an argument from Elsa.
5. More of the sisters getting to be sisters
Even in the show they had their differences, but there was more love in the scenes that they were in together than in the movie. They had been getting to know each other again, and became closer after having been isolated from each other for so long. Instead of Elsa trying to fight her sister off, we should be able to see her be loving to her little sister, teasing her and giving her advice without it coming off as "I know what's best, listen to me."
Whether they take elements from Once, or come up with an idea completely new for Frozen 2, the kids will definitely enjoy it.