I think you are correct in deducing there is a clock conflict. I have got the Dallas library and the RTC library working together by implementing the changes to the RTC library suggested by ForceTronics:
In the RTCZero-master/src/RTCZero.cpp file in your library directory make two changes:
comment out the line
//config32kOSC();
find the line:
GCLK->GENCTRL.reg = (GCLK_GENCTRL_GENEN | GCLK_GENCTRL_SRC_XOSC32K | GCLK_GENCTRL_ID(2) | GCLK_GENCTRL_DIVSEL );
and change to:
GCLK->GENCTRL.reg = (GCLK_GENCTRL_GENEN | GCLK_GENCTRL_SRC_OSCULP32K | GCLK_GENCTRL_ID(2) | GCLK_GENCTRL_DIVSEL );
These two changes swap the RTC library over to using the internal, less accurate but lower power timer.