On some ceiling lights over my fireplace. The only difference is my 3way dimmer is of the toggle type, not the push button type.
If I turn the lights on using the 3way dimmer, it works fine. If I shut it off with the standard non-dimmer 3way, The 3way dimmer will not light the lights again until the switch is turned completely off. Then it turns on the lights completely (no dimmer).
I believe you (and I) will be stuck with this unless we replace the second non dimmer 3way with a dimmer 3way. I live with mine the way it is because I almost never turn the lights on from the standard 3way.