I think it's going to be hard to fit three kids in any trailer. If you look at the pictures of that Schwinn, it looks pretty crowded with just the 4 year old and what looks like about a 1 year old. How often does your 4 year old ride in a stroller? Have you considered using an Ergo or other carrier with your youngest during those times your 4 year old wants to hitch a ride so that you wouldn't need to sit three across?
Those both seem like good choices for two kids. If you can find one used, Trek used to make a "GoBug" trailer that's pretty large and I think it had a stroller conversion.
I'm not aware of any bike trailers that fit 3 children across? One thing that we found to be concerned with while trailer shopping is the head rest area. Some buggies do not have space on the seat for the back of your childs helmet which causes their head to be pressed forward with the chin to the neck type position. If possible try to allow your kids to sit in the buggy with helmets on to make sure they can ride comfortably. Can't remember which brands specifically now but just something you may want to look into before buying.
As far as strollers are concerned what we have found best is the Mountain Buggy or Phil n Teds with a buddy board attached on the back for the third child. The Mountain Buggy is best for rough terrain but you may have difficulty with the buddy board. The Phil n Teds is wonderful to get in and out of the car and takes up much less space and is considerably lighter than the Mountain Buggy.