2 print on demand companies, two different countries: shipping help

[shop-fleurish]

Thank you in advance for your help. I am working with two drop-ship companies: one in the United States and one in the United Kingdom. I have different products with each company and want all of my products available internationally.  So this creates the problem of if you are in the US, the US drop-ship company is "domestic" but if you are somewhere else it is "international" while if you are in the UK, the UK drop-ship company is "domestic" and every where else in international. So I cannot set up one set of rates for domestic shipping and one for international shipping because there are too many variables. I am not sure how to handle this.

Thank you for your advice!!!