I'd suggest checking out the TSA guidelines online. Sorry, I don't have the link available but I know I followed one from my airline's website. There are exceptions to the 3-1-1 ziploc bag rule, such as for prescription meds, saline solution, etc. It's best to review them for yourself as you may have specific circumstances that others are not addressing. And remember, each one in your party is allowed a ziploc bag, so anything that doesn't fit in yours might be able to fit into one of your children's.
Personally, I find it trying to get through security with two children even though they are older. DH wears leg braces and is taken away for an indepth exam and I'm left to overlook his stuff as well as my kids' and mine, and keep an eye on my kids. The 3-1-1 rule isn't difficult just different and something new to get used to.