Then your kids could either contribute to the bill if they are old enough to or be appreciative they have a cell phone if not. When I got my first cell phone, I had to pay for it myself and mobile internet was primative compared to today.
There's more than you and your kids on the network. As already mentioned, data is prioritized based on tower load. Texts not going through also has nothing to do with being on an unlimited data plan with lower priority.