To expand on pbaldy's suggestion.
Each time you add the country table to the query window, Access will suffix the name to make it unique so you'll end up with tblCountries, tblCountries_1, tblCountries_2. This isn't actually duplicating the table. It is simply a visual device to clarify the joins. Now you can create three separate joins. You should Alias the Country name fields as you select them so you end up with ProviderCountry, ToCountry, FromCountry.
PS - it is less confusing if you use the PK name as the FK name rather than the name of the text field. Someone might think your design is incorrect and that they should be joining on Country to Country rather than Country to CountryID. In the table where you have two references to the same PK, then I would use - ToCountryID and FromCountryID. Of course the confusion might be caused because you have used table level lookups but we won't go there now.