[chris (OP)]

Since protons clearly like sticking together in a nucleus, otherwise atoms would fall apart, why is it so difficult to make one nucleus fuse with another?

Chris

[PhysBang]

Protons hate sticking together. However, atomic nuclei have neutrons, and neutrons are really, really sticky as far as protons are concerned.

[JP]

The electric repulsion between two protons is the dominant force only when they're far enough apart.  If you can get them close enough together, the strong and weak nuclear forces takes over and they undergo fusion. (I believe the weak nuclear force turns one proton into a neutron, so that the electrostatic repulsion isn't an issue, and the strong nuclear force actually sticks them together, but I could be wrong.)

The trick is getting the protons close enough together that these reactions occur, which is why things generally have to be very hot and very dense to achieve fusion.

But the take home point is that the repulsive force isn't the most important force once you force the protons close enough to each other.