Dear Jeremy,
Do I understand you correctly that if any product from category 114 OR from category 109 is in the cart, then you don't want to ship to eastern Europe and UK?
In that case, your categories check is wrong. In particular, your check "Categories==list(114,109)" means that this rule only applies if the customer purchases products from both categories, and from no other categories. What you rather want is:
Name=No shipping to xxx; Condition=contains_any(Categories, 114, 109); country2 in list("BG", "CY","EE", "GR", "LT", "LV", "RO", "RU", "SK", "SI", "TR", "UK"); NoShipping
That condition (please notice the important "Condition="!) means that the rule will apply if category 114 or 109 is among the categories of all products in the order.
Best regards,
Reinhold