I would not read too much into this. This seems more thoughtless and impulsive than anything else. And the "kiss my a**" comment could have been rude and mean but it could instead have been impulsive or even a very bad attempt at awkward humor because she suddenly was told that your husband wouldn't like it (her mind was on pleasing you, not on passing muster with him, so she probably flubbed her response).
I think it's important to note that you took a lot of care to let us know about her depression, anxiety and multiple surgeries, so I think you are inclined to tread gently over this issue with the sticker, and I would do the same. Yes, it was intrusive and inappropriate and should never have happened. She was wrong. But you can choose to be pissed at her or take the high road and shrug it off as an act by someone who might not "get" why it's intrusive. Why wouldn't she get that? Depression, anxiety, repeated medical issues can make a person at least temporarily lose some of the "filter" that helps us think before we act, and helps us stop a minute and say, "Wait, maybe I should just hand her the sticker." Maybe there's no excuse for what she did but that is at least an explanation. If she's a very emotional person, with all the things she has going on in her life and her body, she wasn't thinking when she did this, so it wasn't some intentional slight or attempt to manipulate you. You said it yourself--she thought she was doing something nice. She was wrong, but you can choose to respond with being pissed or letting it go.
(Added: I'm not saying she gets a pass on inappropriate behavior because of being depressed etc., but I also think this is not, as the saying goes, "a hill to die on"--or a reason to push her away with some big announcement of how wrong she was. The sticker's gone. If she gets persistent about trying to replace it again or wants to argue about it, that's different, and I'd distract and divert if that happens. But in itself, I'd let the sticker issue go, unless it's part of some larger pattern of her overstepping boundaries, and you don't say there's such a pattern.)
I would not make some statement to her about it or announce that the sticker was removed. I would just say nothing and if she notices the sticker is gone and comments on it, just say, "Oh, Husband removed it since he didn't want any stickers on the new van." Then divert her to another topic. If she wants to argue about it, don't engage at all, just say thanks for saying you feel so close to me.
If the sticker made some statement that is political or religious etc. and she starts to say "You disagree with me" and get upset, I'd repeat that this is about ANY sticker on the new vehicle and not about content one way or the other. I wouldn't get into any discussion of the sticker's content with her. If it's some innocent thing like, oh, a "stick figure family" and she meant it to convey that you're all one big family, thank her for the sentiment.