How successful were attempts to control the development of nuclear weapons between 1949 and 1980?
Early on, these attempts were not successful at all. As time went by, the attempts became more successful.
For example, President Eisenhower was not very successful at all in either his "atoms for peace" proposal or in his "open skies" proposal. Both of these can be seen as ways to reduce the spread of nuclear weapons. Obviously, they did not succeed in any meaningful way as the US and the USSR continued to build more nuclear weapons and to create more powerful weapons as well.
Towards the end of the period in question, these attempts were more successful. There was the nuclear nonproliferation treaty that took effect in 1970. There were the SALT talks of the 1970s. Both of these had some impact on reducing the spread of nuclear weapons.
Of course, the world still has huge numbers of nuclear weapons. The major powers all still have nuclear weapons. Pakistan and North Korea have gained nuclear weapons since 1980. This makes it quite clear that the efforts to control development of nuclear weapons were not very successful overall.