Nicaraguans love children and dote on them. We have both traveled with babies and small children in Nicaragua [1] with relative ease. You may find that traveling with children opens doors and forms new connections. That said, your children will have to endure the same lack of creature comforts, change in diet, and long bumpy bus rides you do.
Disposable diapers are expensive but readily available in supermarkets, as are powdered milk/formula, pacifiers (pacificadores or chupetas), and bottles (pachas). Ask your doctor and consult the CDC about malaria prophylaxis for your child.
Perhaps the most important thing to pack is strong sun protection for delicate skin and disinfectant hand soap or foam. Travel with a stroller is half useful and half annoying, as Nicaragua’s sandy and cobbled streets frequently require bigger-wheeled strollers that are thus harder to pack and carry around.
Make sure your rental car company can provide a car seat for you, or you will be required to bring one (we highly recommend it, considering the danger of Nicaraguan road travel).
Links:
[1] http://www.moon.com/destinations/nicaragua