I love Cove Bar. One of my favorite places in DCA to relax. Their lobster nachos are great, as are their drinks.
Kids cannot sit at the bar itself but are allowed to sit at the tables. It is fun to people watch and you will probably have a great time.
Just remember it is called Cove BAR. You will see kids there, it is a fun atmosphere, and it is at a Disney park (so most are on their best behavior) but please remember a lot of adults go there to drink. And I don't mean 1 and done. The ratio of adults to kids is well over 50/50 (I would say 90/10) and the closer you sit to the bar itself the more adult conversations you may end up hearing. It is popular with the younger 20 somethings who may not filter their conversations for young ears, esp after a few strong fruity drinks with a group of friends. That is just the Cove Bar crowd some days.
This is not always the case. I have been there many times where it is fun for the whole family, I just want you to be prepared.
Helpful hint: Cove Bar normally has a line. If you get offended by the people in line, or notice several groups of young people ordering multiple drinks I would reschedule your visit. Also, the earlier you go the better it is for food, shorter lines, and the less likely you are to run into the rowdy crowd that likes to show up after 6pm.