I see my ATF 3-4 times a year when I am in her city and she always brings up her daughter and we talk about how she is doing. It's always a nice moment and conversation. Is it appropriate to bring a gift for her daughter next time I see her (she is really into soccer)?

I'm sorry but bringing your child around your clients........That's not cool. Let alone allowing the client to by your child a gift.

Where do you get that the lady is bringing her child to appointments?????

I've had hostesses bring up the subject with me. See my recent post:
http://www.theeroticreview.com/discussion-boards/ter-general-board-12/re-i-try-to-avoid-married-providers-1011482
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In the current case, there is a lot of missing detail. I did NOT get the impression that the child was brought along, introduced, or even on the premises. Also, is the daughter 2 yo or 22 yo? "I'm so happy that my daughter just got into a great pre-school program for 2 yos!" versus "I'm so proud that my daughter just got accepted into law school!"  
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In either case, "Here's something to get your daughter a nice present. (A Barbie doll versus a "Bar Exam Test Prep" book.)
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I.e., I think that there's a way to handle such gift giving nicely and not weirdly.

She doesn't bring the child- she speaks of her.

but only with gals I have gotten to know on a personal basis.

I learned that a woman that I was seeing had children.  We discussed them when we'd meet.

I know that would be appreciated.  

You’re very thoughtful. My friends have sent my children gifts over the years & it makes me love the more. You’re a sweetheart. I am sure they both appreciate your thoughtfulness.

Again mixing business and life can have risks.  There is the story of a famous Minneapolis provider who was befriended by a client, met her kids, helped her out financially etc, but then became her stalker and allegedly ratted her out to the cops.  Later she learned from the guy's brother that he suspected him of murdering his former girlfriend.

I don't think he said she brings the child with, I think he said she talks about the child. I do not have kids, but clients do often bring treats for my dogs, which is very thoughtful.

I think it would actually be sweet, shows you care about her and her little family. If she’s into soccer then get her something soccer related.

He talked about buying milk and diapers for her kid. He also suffered from what we called Random Capitalizatiion Syndrome. What a fucking weirdo.

that the provider brought her child to see him-sigh...

For her daughter. It was fun.

daughter through the mother is the best bet to avoid any awkwardness.  Just tell your provider not to tell her daughter that a guy who is one of her sex customers made the gift possible.  The joy is in the giving.    Lol