Is uranium glass more dangerous if it is broken? Does breaking the glass release the radiation?
No, uranium glass is not more dangerous if broken. The uranium dioxide is in the glass at the molecular level. It is just as much a part of the glass is the melted silica sand that makes up the majority of the glass. It cannot be separated once it is added to the molten glass, and no extra radiation is released if it is broken.
With that said, safety precautions still need to be on place if you are cutting or grinding uranium glass. Glass dust is dangerous to inhale whether it is uranium or not. An N95 mask is required for cutting glass, and ideally a water system and/or some kind of ventilation.
A necklace I made by cutting out the flowers from a broken Fenton poppy lamp. There was no increase of radiation once the lamp was broken. I took all proper precautions in cutting the glass so I would not inhale the dust