Hi, Amy! At my highest weight, I was over 300 pounds, and in all the times I visited Walt Disney World, I never had a problem doing any of the attractions with my girls. In many cases, I would put the girls in front of me, and I rode behind them; but on attractions where I thought my youngest was too young to go with just her sisters, she always fit with me.
One thing you need to be careful about are attractions where you pull the lap bar down to you. If you are riding with a small child, I always found that I didn't feel my girls were safe on some of the attractions (like Big Thunder Mountain Railroad) if they rode with me, as the bar didn't come down far enough when it had my tummy to stop it from securing the little one. I made sure the kids rode together on those attractions.
On boat rides, I always sat in the center of a seat, and I requested not to be in the rear or the front of a boat. This helped me feel more comfortable about balancing out the weight in the boat, but honestly, you'll be fine in either the front or the back. In theatre type of seating, I would sit on the edge of the seat and slide back. It helped me get adjusted!
You couldn't find a place friendlier towards people who are Pooh sized than Walt Disney World!
I hope this puts some of your concerns to rest, and I hope you have an absolutely awesome vacation with your kids!