What's the right balance of allowing children to have fun (i.e. running around in the building before/after service) and safety?

We have been blessed with many, many children at my church. And to date, we've been very relaxed on allowing children to run and play in the building before/after church. As a member of the security team, I want to be sure children feel safe, welcome, and free to have fun, but also want to balance this with safety of themselves and others.

We've had children fall down, step on others' toes, run into strollers (with babies inside!), etc. Also, we've had such a relaxed culture with some of this stuff that sometimes parents don't even know where their child is or what their child is doing.

I was personally taught not to run inside any building, especially church, but I don't want kids to feel like they can't have fun.

We're in a new building now and there's even _more_ traffic congestion where people congregate before/after service as well as a lot more hard objects to fall and bang heads on.

1) What's the right balance of fun and safety?

2) If children should not run in the building, and we believe the best way to prevent this is having parents be more attentive to where their child is and what their child is doing, how do we communicate this to parents in a way that is edifying and helpful?