Take a moment to look through the diaper bag you have now and figure out if there is anything you carry around that you really don't need. (Think about the size of an average purse --- what the heck is it that we carry in those things?!?! Men throw a wallet in one pocket and a cell phone in the other and they're good to go!!) With my first child, I carried a hug diaper bag filled with "just in case" stuff. Yea-- if you are spending the day at a theme park you need a bunch of stuff, but think about where you usually go during the day-- you probably seriously only need maybe 2-3 diapers, some wipes, and one bottle or sippy-- and maybe some Cherios. Everything else can be stored in the car. I kept a diaper bag in the car with extra diapers, a ziplock baggies full of wipes, an empty bottle and/or sippy cup, and a change of clothes for each family member in a ziplock bag. I even kept a big t-shirt for myself in case I got spit up on me. Most of the time, months would pass between times when I needed anything out of the car bag, but it was nice to have it there. Even with 2 kids, you really only need to carry with you a couple of diapers per kid, a container of wipes (I fold mine over and keep them in a sandwich size ziplock now because those plastic dispensers are so bulky), and some spit up rags for the baby. Buy a soft sided lunch box to tote sippies, bottles, and snacks if you will be out for a while and think you'll need them.
As for other advice, get a comfortable baby carrier-- I used a sling but not everybody likes those. It's much easier to help the toddler's needs if you have the baby in a carrier rather than held with one arm. It's insane for the first year but it gets easier when you can put them baby down (to crawl/walk) when he's old enough.