If your husband is not travelling with you, you need a signed form with his permission, in order to leave Brazil on the return trip. The form has recently changed so be sure you have the correct one. It is now good for only one time/use/entry/exit (and it has been reported it will be retained/taken at passport control in Brazil, perhaps one on entry and definitely one on exit).
Brazilian citizens must enter and leave Brazil on a Brazilian passport, so if your kids are registered as citizens, plan to have both their U.S. and Brazilian passports.
Take lots of mosquito repellent. It is more expensive in Brazil. Dengue is still a risk. Those mosquitoes bite during the day as well as at night with the others. However, DEET products, the most effective, are considered a risk to young children.
Adults probably should have (basic travel shots) tetanus, typhiod, hepA, etc., but not yellow fever, unless visiting an area that has it You should consult a physician specializing in travel medicine, preferably one who has personal experience in Brazil, instead of consulting amateurs on a travel forum, though, especially regarding the kids.
Most Brazilian cities have sidewalks in such bad repair that using a "normal" U.S. stroller, esp. an umbrella stroller, is almost impossible. Don't know if you plan to tour or just stay around your family's house, but if you don't want to carry both the baby and a tired toddler, get a good, maybe double, carriage with the biggest tires you can find, or think about backpacks to carry both kids.
Take, in a carry-on, enough interesting stuff (coloring books, paper, crayons, puzzles, books, etc) for the 5 year old to do while still awake on the plane.
Get as much sleep as you can before the trip, so as to have patience and stamina. Any trip with connections can end up as 19+ hours of travel, so you'll need it.
and....have a great time !
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