I did the same thing to one of my tubes. Bent and broke off the inner part of the stem. Rode the bike after I did it but my husband replaced the tube when I told him.
For some reason the pump head tends to shoot off the stem when my husband fills tires and he uses a special hand position to keep from getting his fingers smacked against the spokes. When I fill tires this shoot-off thing does not happen so I have not had to learn his special trick. Too bad, because it sounds like you would benefit from it if I could pass it on.
What I do to remove the head is wiggle it slightly from side to side and it gradually loses its hold and just falls off with a whoosh. Maybe that would work for you since the same pump that explodes off for my husband falls off gently for me.
To put the pump on I put my left forefinger and thumb around the tire and steady the head of the pump on the stem. With my right hand I press against my left for stability as I flip the lever with my thumb. This seems to help as I have not bent a stem since adopting this technique.
I am sure you will get better and easier to understand info from some of the more experienced riders. I am just a newbie who has finally made friends with the pump.