This came out to be longer than I'd intended, so, direct answers to the question:
Keep the focus on the decision to buy the coat and her reasons for doing so. DO NOT focus on what you imagine the broader significance of that decision to be, nor your personal judgment of your daughter.
Ask questions about why she chose as she did, and what she knows about the process of manufacturing the coat. DO NOT lead with your assessments of her quality as a person or her beliefs about treatment of animals.
Do not even suggest that being a part of the family requires that she believe exactly as you do, and deviation from those beliefs automatically indicates that she has chosen to be kicked out.
Determine whether or not voicing your opinion is really all that you want to do, and if so then don't do more than that. Voicing your opinion does not require any response or discussion. If you do want something other than that, pretending otherwise won't help avoid a dispute, and my advice for how to talk to your daughter would be different.
Background and rationale for my answer:
I see four major issues that are likely to turn any conversation into a more heated dispute:
"What bothers me is that this choice of hers is in conflict with what I believed are our family values."
This framing implies that, if she feels the coat is acceptable (for whatever reason) then she is defined out of the family. It may or may not be what you mean to express, and you may or may not be OK with that implication, but the position that "if you don't recognize that buying that coat makes you a bad person, then you're not really my daughter anymore" isn't one that you can plausibly throw out there without expecting it to cause a dispute.
It may be the case that she really has reconsidered her values and believes differently from you and the rest of your immediate family. But what, exactly, does it mean to you that she might hold that different belief? It might also be the case that she's unaware of whatever factors informed your ethical concerns, and so doesn't realize that she's crossed a boundary you both believe in. Assuming that she has not only intentionally transgressed but also willfully abandoned a key part of being your daughter will only intensify any discussions or conflicts that might arise.
2. It's not clear to me what you really want here.
I don't know you personally, so this may not be a fair take on your position. But, in my experience, people are rarely satisfied just to express their opinions on topics like this one. Far more common is when someone wants to express their opinion, be acknowledged by the other party as being totally correct, and have the other party agree in the end that they are wrong to have done whatever they did. In addition to that being the typical way I've seen scenes like this play out, the tone and focus of your question reinforces my impression that you're looking to do more than express yourself.
You could easily mention to your daughter "That's a nice coat, but I think that it's morally wrong to wear animal fur", and have that be the end of it. It seems to me that you are planning for, if not necessarily expecting, there to be more to the conversation after that. There's nothing wrong with that, but if you do have some other motivation or goal, that would need to be explicitly addressed (and, as mentioned above, I can't guess very well at what other goals you might in fact have).
3. This may be clearer for someone actually in your family, but it's not clear to me where the line is on your animal rights position.
You eat meat, so it would seem that you are willing to accept animals being raised and slaughtered for human benefit. You state that you tend to buy ethically raised meat, which suggests that at least some of the time you do not.
From your question I believe it likely that you are interested in the conditions in which animals are raised, and the fur industry (generally or in the specific case of Canada Goose, either way) is over the line for you. But it may not be as clear to someone else where you feel that line should be. If you sometimes buy unethically raised meat, why can your daughter not buy a single fur-trimmed coat one time? I would imagine that you can describe your positions more fully than in the question here (that much context would be off-topic here anyhow), but it could easily be the case that your complete ethical position is not/was not clear to your daughter.
4. Her choice of coat is probably not about you.
You know your daughter better than I do (which is to say, at all), but I think it's probably not the case that she was intending to send any sort of message to you in choosing the coat. Your feeling that
[…] by wearing this coat all the time, she is going to great lengths to reject not only the way she was raised, but in essence, me.
completely shifts the discussion away from both being about her decision to buy the coat as well as the broader issue of animal rights. Your position seems to be that, even more important than the underlying ethical issue, the main problem is your personal offense at her choice to buy the coat. Wearing a winter coat in the winter is not exactly "going to great lengths" to do anything, regardless of how many coats she owns or how much she likes them.
You could be totally correct, and this was a gesture aimed at you. But if that was not the case, then fundamentally mischaracterizing your daughter's decisions and motivations makes a fight a fair bit more likely.