I felt the above scene is a little strange. I wonder why she wanted to get there?
The followings is my interpretation.
They made Episode 1 as the new start for Violet to find out what "I love you" means.
At the same time, they made it as the improvement of her arms, too.
At the beginning of the episode, she found out her arms had had been replaced with metal ones.
She tried to write words down in the hospital. As the result of training, she got able to write words. However, her writing speed was still very slow (it's going to be contrast to her typing speed) and the nib was shivering.
She couldn't keep up holding a cup, then she thought she was disable to do such things yet and needed to be used to them.
Hodgins told her to live with the folks of Evergarden, that made her think she was leaving with them and away from army because of her disability of her arms.
When she knew she had not been needed as a weapon anymore, she got hopeless and wanted to be discarded.
Then, she sorted a pile of mails for all the day.
She delivered mails.
However, she couldn't use a knife well.
So then, she tried to get on the roof, for the training of her arms. It's the reason why she got there.
Probably, meantime, she wanted to think about her future by looking far away from there.
At the same time, they showed she had enough strength, probably more strong than normal people.
Of course, this is just my opinion. Yours are always welcome.
By the way, here is another interpretation. It's so great.