with a 1 yr old baby, I think you need to go to the disneyland in both days. Cos last week, I went there, arrived at 11:30 and left at 5pm, we barely finish the part for young children. Cos you need to settle down for them to eat lunch, and they might feel sleepy etc. So I do suggest you to go there early. It might be too demanding for you 1 yr old to watch the firework.
Also, there is hot boiled water inside the nursery room in the Disneyland (free) but do remember to bring room temperature water becuase it is about $16 for a Bonaqua.
It is so much fun when your child smiles in the park, although it would be tiring for you, I think it worth it.
BTW, weather forecast says it might rain, so maybe you need to bring the raincoat for your elder kid and a rain cover for your stroller. Where warmer cos I found it quite windy there!