As your child is NOT travelling, do not let that pump out of your sight. TSA may or may not be curious about the pump (mine is a PNS), just tell them what it is. (I find that male TSA agents hear what it is and will wave you right on through -- they don't want to open it up. Women may be a bit less squeamish, but IME not much less.)
Keeping up your supply is certainly a valid concern, but the more immediate one is engorgement. If there is a major flight delay or if the bag containing the pump should be delayed, you would be in rather severe pain by about 10 hours without the pump. Don't take the chance. Carry the pump, power source, and one set of horns, tubes and bottles on your person.
Are you carrying your milk home? If so, you'll need to keep it cold but not frozen in your room, and have a couple of freezer gel packs frozen to keep it cool when it is time to return home. You can carry the chilled milk in a lunch cooler. Put the gel packs in your checked baggage on the way down, and ask the hotel kitchen to hard-freeze them for you overnight for the day of departure.
I just finished a business trip with my pump. My production is down somewhat since DD is a year old, but in three days away I pumped 52 ounces that had to be taken back home. I used a 12 can soft totebag cooler to hold it all, with the ice needed to keep it cold. Be sure to carry milk in a separate bag through security, because TSA *will* want to look inside if it is a fairly large quantity with freezer packs.
For travel, I use the Lansinoh double-zipper milk freezer bags (with the air pressed out), stacked flat inside Glad deep rectangle plastic freezer containers. That takes up the least room, I find, and I've yet to have a problem with them leaking.