Re: transporting breast milk
it depends on whether you're freezing the milk or not. you can strategize about what would be best. the danger with freezing is that if it thaws, it has to be used right away.so i know some people freeze, then pack in a cooler with dry ice and check it. i found it easier/less worry-inducing to leave it refrigerated, then carry it on in a cooler with ice. but i also only travelled with 3 days worth, and even some of that went bad before we could use it. just due to the uneven refrigeration, i'm guessing.
you'll have to check with your airline about the rules of checking dry ice - there might be a fee or labeling requirements.
for just a 3 hour flight, i would probably freeze all but the last day's worth, pack in dry ice, and check. then for the current day, pack a small cooler in your carry-on. i put milk bags inside a gallon zip, then had a separate gallon zip for ice. i dumped the ice just before security and filled back up after security - if any ice melts you face problems with "extra liquid" (idiotic but true).
it is worth just spending a moment thinking about what will happen if they lose your checked bag; some people prefer to ship by fedex or another trackable method, which is expensive but possibly more reliable.
Nursing, pumping, cloth-diapering, babywearing, working professor mama with the awesomest SAHD ever.