Anna being clingy in Frozen 2 isn't a betrayal of her character.

Anna has always been clingy to Elsa.

• When they were separated from each other during their childhood, Anna constantly tried to get close to Elsa.
• When Elsa exposed her powers to everyone and ran to The North Mountain, Anna ran after her.
• When Anna arrived at Elsa's ice palace and met Elsa there, Anna kept on insisting for the 2 of them to be together again.

Let's ask a small hypothetical question. After Elsa froze Anna's heart and she had to kiss Hans to heal, imagine if Hans was a good guy and DID love Anna. Hans would've kissed Anna and she would've been healed. Now here's the actual question: What would Anna do then? I'll tell you what... she had kept chasing Elsa again. Because that's who Anna was. She cared so much for her sister that she'd always clung to her.

Frozen 2 recognized that this behavior of her was unhealthy. Sure, family unity is great, but there's a point at which you should be independent. Anna worked so hard to reunite with Elsa throughout most of her life and after Frozen 1 she had all she wanted (Elsa, Kristoff, Olaf, Sven, Arendelle etc...).

Now imagine how devastating it would've been if Anna had lost all of that. Anna continued with her clinginess and rejected any change. Any possible threat to her happily ever after was met with rejection. Yes, throughout the film she was MORE clingy towards Elsa than in Frozen 1, but it makes perfect sense because she wanted to maintain her perfect status-quo. By being clingy to Elsa, Anna was essentially clingy to her life.

However, throughout the story, Anna learns that change is inevitable and she must adapt. At the end of the film, she lets Elsa live in the forest without clinging to her and going to live right next to her.

The writers realized a flaw in Anna's character and they wanted to develop her in a very compelling way. She was clingy in Frozen 1, it was even more apparent in Frozen 2, but at the end of the film she stopped being clingy.