I'm so sorry you are experincing this much criticism. I have only had a handful of snide remarks and usually from people not very close to us. How hurtful to not have your family's support.
You are doing the right thing. Her face will fade and with time they will understand. Try to be confident in your decision. The above poster is correct. Your daughter will thank you.
As for going out in public, that is your choice. My son and I do. I feel like we are a PWS advocate team wherever we go. People can not help but ask questions. I do my best to answer them confidently to demonstrate to my son that he has no reason to be shy because of his face. Our conversations go something like this:
Random stranger: What happened to your baby's face?
Me: He had a laser treatment.
Me: He has a large birthmark called a Port Wine Stain on his face.
Stranger: Will it fade? My son/grand baby/niece had a birthmark and it faded on its own.
Me: No, it will not. That is why he has laser treatments.
Stranger: How lucky he is that it can be treated.
Me: Yes, we are fortunate to have such options available.
This conversation has happened dozens of times. Often in the grocery checkout where your are confined next to a stranger who can't help but ask. Or if I see curious stares, I start the conversation. More than once, someone has shown me their birthmark and wished they had treatment.
It is going to be ok. It gets easier and she will thank you.