Well the problem is with your router. Just google how to open NAT and it should show you how to fix the problem.
If your NAT is closed in general you will get a worst connection and experience playing games as people will have troubles connecting to you as you will have troubles connecting to them.
The weird thing is that is sounds like your NAT only closes when you have the second 360 on which shouldn't be the case, if the NAT it is closed it is always closed and vice versa.
My friends have two 360's connected to their router and play online together all the time so I know for a fact it can work without a hitch.
The definitive evidence that video games turn people into mass murderers
