My suggestion to you is to wait a little bit and let this kids to grow.Holding a shotgun for a 10 and 11year old it's a hard work, especially when you have to shoot a moving target.
Starting at this age is risky because of poor physical condition, they will develop bad habits.Even if you have a small gauge gun will not resolve the problem.Taking out bad habits is very hard and those habits can remain for the entire life.
If you have a chance to come to Atlanta I can meet you at the range and tell you other things.My first Olympian. Collyn Loper from Birmingham Al. and the actual Skeet Olympic champion Vincent Hancock learn about the Olympic style shooting at age of 12 by being involved in my junior program.
All the best
BIll Erdoss
Http://shotguncoach.com