Some of our distributors do not allow us to sell products beyond the US borders.  Other distributors are fine with it.  Is there a way to specify which products can be shipped internationally and other that can't.  I tried setting up the groups but it was a little confusing.  Ideally, I would like to have 2 groups 1) Products that can be shipped to US only and 2) Products that can be shipped to the US and Internationally.

 Any recommendations?

In the product editor on the Shipping tab, you can use the Limit To Shipping Region selection.  You can create a region for just the United States.  If you have many products, it might be easier to export your products (under Global menu), set the LimitShippingRegion field and re-import.

I set this up several months ago on my own site.  All products taht are US-only are designated as such on my ship tab, but it doesn't work.  Int'l customers still order these items.  Is it because we use variant inventory and the variant matrix?

Should still work.  Several sites are using this.  I suggest you enter a support ticket so it can be researched.  If it is a defect, it will be corrected.

That is correct.  It displays a message and does not allow them to check out.  It will also display a message on the cart page if they enter an address to get a shipping quote.  It is based on the shipping address which is usually not known until after they have added items to their cart.

Though it usually possible to determine country based on IP address, there are issues with this including those shopping outside of the country who may want to ship items domestically such as military personnel.