Networked switches just work differently than nonnetworked switches. The switch has to always have a small amount of power or it can’t hear the next “on” command the comes over the network. But you still need to cut the load to the fixture. So you can’t just swap out what you have with the new network switch. You may actually have to change the wiring around a bit.
And your instincts are absolutely right, when you have a three-way switch, you have to replace the old auxiliary as well, otherwise it cuts off power to the new master.
It sounds like the best thing may be just to bring in an electrician. But in the meantime, read the FAQ, and it may help clear up a bit of the confusion (this is a clickable link)
Automated Switches: What should my wiring look like? (US Version)