If you open your RAW file into Photoshop through ACR as a smart object layer. The smart Object layers object will be an embedded RAW file with your ACR settings stored in the embedded object. Anytime your editing the Document in Photoshop. All you need do is double click on the layers smart object content icon in the layers palette. The embedded RAW file will be open in ACR with the settings you set and are recorded in the layers object. All you need to tis change the setting to what you now want and Click OK in ACR when you Click OK in ACR the smart object ACR setting will be updated and Photoshop will render a new set of pixels to be used as the smart objects layers pixels. As far as I know you can not trash the smart object layers ACR settings. You may be able to reset them to your Defaults. The settings are not your RAW files XMP sidecar file they in the layers embedded object which has a copy of you RAW files and ACR settings for its conversion..
If the XMP ACR file is older than 2012, you need to reset the file to default to have ACR use the new ACR settings - well worth the effort to do this.
I don't understand what an ACR file is. I am working with the latest version of Photoshop. I'd like to know if I can somehow extract the xmp file from photoshop (the one that is associated with the PSD document I am working on - I can still access my image through camera raw because it is a smart object). Usually when I edit a photo in camera raw, there is a CR2 file and an xmp file. I'm not sure why the xmp file didn't update the changes I made in camera raw when I started editing the CR2 image again. I basically want to have a fool-proof work flow so I don't lose any recent changes I've made to the image. I usually have a PSD document that I'm working on (with the image as a smart object), and I thought it was saving any changes I made to the corresponding CR2 file & xmp file. Am I misunderstanding this?
You are misunderstanding this.
When you open your raw file in a Photoshop smart object - the smart object contains a copy of the raw file and the adjustment info for camera raw.
The original is separate to that file. It has to be that way as you may use the same raw file in several different PSD documents (or as separate layers in the same document each with different adjustments) and you do not want those reflected in the original.
You could however place the raw image in your Photoshop document as a linked smart object (use Place Linked). If you do that any adjustment you make to the raw file outside of Photoshop will be flagged in the Photoshop document with a warning triangle.
If you right click the layer and choose "Update Modified Content" then the layer will reflect any changes made in the original RAW file xmp.
Conversely if you double click and open the SO to make an adjustment - then those changes will be written into the original XMP file (i.e. you are updating the original raw file xmp).
It seem more like you do not understand smart objects.
ACR is a plug-in and a Filter. The are many files involved when you use ACR. I would not call any an ACR file. You have lens profiles files. Preset file, RAW files, Saved ARC setting in XMP or in ACR's Data bases. You have converted raw data in Photoshop documents as a layer, a normal layer or as or smart object layers. Photoshop is a Document editor not a file editor. ACR is a RAW DATA Converter. Photoshop and ACR can save Image Files. Not all Smart Object layers objects are the same there are many types of objects.
What do you mean by an ACR file. Is there such a file? I have never see a file with and extension like .acr