I read what Nona wrote and feel the same way about both sentences but as to the Number 1 sentence, the phrase "the woman in a pair of white gloves" conjures of an image of a woman engulfed (or covered) by a huge pair white gloves.
So, I think it is better to say, "The woman who has a pair of white gloves on is my English teacher."
Believer wrote: So, I think it is better to say, "The woman who has a pair of white gloves on is my English teacher." In my opinion, your sentence is too wordy.
If you want to rephrase the sentence, it should be "The woman wearing white gloves is my English teacher."