The suggestions above are all good, particularly using a soft hood. If you don't want to do that, a black towel is useful for draping over head/shoulders to cut down on reflection. Brace against the glass or adjacent walls to avoid having to rely on a tripod.
Pick your battles. Exhibits like the king crab/pinecone fish and octopus exhibits are REALLY dark, and as the animals react poorly to flash, are designated "no-flash zones." Add in fish that are moving around a lot, and it's easy to come away with a bunch of mediocre shots. The thing about that aquarium that really sets it apart from other similar institutions is its emphasis on freshwater critters. Many of these tanks are small, well-lighted (mostly to support live plants), and shoot surprisingly well if you can time your visit to keep away from crowds.
Also, no offense, but if you're taking kids along, you might consider just letting them enjoy it instead of having to work around your photo sessions...