If your having her write these words hundreds of times, she is likely being overly stimulated with this. While children do regress some over the summer, its normally picked up within the first month of school.
My main concern, is that as you mentioned you have very little patience with this and are making things worse. The last thing you want to do is cause her to regress and refuse to do the work. Right now she feels bad enough that she is struggling......but add on the extra work she is being required to do and your anxiety (Which she can sense and feel) and she is likely a bundle of anxiety and fear over the whole matter, not a good mixture when you want her to learn something.
The first step is to calm down, if she knew it once.....she will know it again. But pushing is only going to cause more harm. As for Sylvan, to be honest I love this program even for children who are not behind as school is very difficult to begin with for some children and that extra one on one often helps children get caught up quickly in a fun and non stressful environment. And in most cases in a short amount of time they can have your child at or above the average! Sylvan is a huge helping hand to keeping children interested in school and getting them back on track.
If you have the resources to use Sylvan then yes it would be helpful in more ways then one. I would also suggest that you speak with them on the best way for you to help her with her homework when she is not in Sylvan so you can make sure you are helping her in the way that is most beneficial to her learning.
I know it is frustrating and scary when your child begins to fall behind, but try to stay calm and remember if she knew this once she will learn it again.