***Not a teacher***
Actually, the commas in the OP's context are used to surround something additional and descriptive. The words in between can be omitted. I agree with Mike in the first reply. If you omit 'wearing a hat', the sentence wouldn't make sense because there is 'which I told her to remove' in the context. The two commas should be placed before 'which' and after 'remove'. But then, it wouldn't make sense, right? Because you follow it up with seeing the hair and offering the price so the commas aren't necessarily necessary. Just saying.
Answer is: no, the comma before 'wearing' isn't necessary.
You could break it up.
"And a woman came into my store, wearing a hat which I told her to remove. I wanted her to remove it so that I could see her hair and offer a fair price for it."
In the first sentence, I used only one comma because the other comma is replaced with the full stop to end the sentence. The comma is just to separate the main sentence with a description.
'I, a boy, am going to post this post'. I just added information that is unnecessary and it could be omitted. 'I am going to post this post' practically has the same meaning.
What you would do with her hair, I don't know! Wigs?
@Matthew (I like your pic)
"In English-Chinese dictionaries, the two verbs translate the same, causing confusion."
The first comma used is because you started with a preposition. The second comma is to separate the main sentence from a description. The sentence works fine by "In English-Chinese dictionaries, the two verbs translate the same."
The sentence "In English-Chinese dictionaries, the two verbs translate the same causing confusion." Commas are actually used to separate parts of a sentence and to give the sentence a pause to make it understandable. If you said "In English-Chinese dictionaries the two verbs translate the same causing confusion", would it make sense without commas added and by talking at a steady monotone? Not really... So Matthew... the comma is best to stay where it is, unless you want to omit it along with 'causing confusion'.
***Not a teacher***