One trick when reinstalling a tire/tube is to use some very, very dilute dishwashing detergent in a spray bottle. It will lubricate the tire and tube so they will slip over the rim, and not get pinched as readily by the tire tool/levers.
Heavily spray the tube and tire when reinstalling. There should be a "bit" of air in the innertube, so it will tend to form to the tire, but not so much air that it will bulge out and get caught/pinched by the tire/bead as you are levering or thumb pushing the tire bead back on.
Some tire rim combos require tire levers-be careful when levering the tire bead back on-you need 3 levers in some cases- one on either side, and one to lever in the middle.Make sure you push that tube "in"(not too much air in it) before levering that tire bead back on.
Another trick-pump the tire up to maybe 20 psi-then bounce it all the way around a bit to "seat" the tire and bead. Drop the pressure to 10 bounce it carefully , then pump to 40 psi-bounce, 60 psi-bounce.
Make sure that the valve stem is at 90 degrees-not bent.
Make sure the bead is more or less even all the way around-the same amount of tire should be invisible all the way around.
Some folks say detergent is too hard on rims-never noticed that to be a problem. Rinse/hose your rim with water after this(soapy rim is slippery-hurt your braking.
Charlie