I would just switch to another cup they are happy to use (for example, something they already use for water or other drinks). At 2, they don't need loads of milk each day, so I wouldn't be too worried if their milk consumption goes down if they initially refuse the new cups. They'll be getting plenty of nutrients, including dairy, from other sources, so it shouldn't matter too much. We found initially that straw cups worked the best. We use the Moma straw cups, which have a spill proof straw that seals and holds the milk in the straw even if they aren't sucking out of it, so they are easier to use, especially for things like bedtime when a sippy cup might not work. We had a few false starts, but then my daughter happily used the straw cups instead. So I would just make a plan and stick to it. They will get used to it with a little bit of time.
