I'm not familiar with vinyl fencing. But I'm sure there must be some way to reinforce them. I'd go talk to someone from the fence department at Home Depot (or whatever home improvement store of your choice ) and find out what can be done.
If the posts are already in I would just buy some wire fencing (like stucco wire) and put that along your side of the fence. It won't stop them from bouncing off the fence but more likely to keep them from getting out.