What is the force that involved in the interactions that allow nuclei to decay?
The weak nuclear force is responsible for beta decay.
For nuclei heavier than hydrogen, there needs to be a balance between the electromagnetic force and the strong nuclear force. The electromagnetic force make the positively charged protons repel each other. The strong nuclear force binds protons and neutrons to form the nucleus.
If a nucleus has too many protons or too many neutrons it is unstable. The weak nuclear force can restore the balance by converting a proton into a neutron, a positron and an electron neutrino. It can also convert a neutron into a proton, an electron and an electron antineutrino. This is beta decay.
Elements lighter than iron, fusion reactions to create heavier elements release energy. For elements heaver than iron fusion reactions to create heavier elements require additional energy.
Some heavy nuclei which are unstable emit alpha particles. An alpha particle is a helium 4 nucleus which is very stable. This works by 2 protons and 2 neutrons bind into a helium nucleus within the heavy nucleus. Sometimes this alpha particle is able to escape via a quantum tunnelling mechanism.