The US however, would also have a very difficult time launching an invasion of North Korea because of a huge manpower disadvantage and the fact that they'd have to cross the biggest mindfield in the world. And the Koreans would just stack up troops on the border if the US began any sort of reinforcement of Korea.
A sea-borne invasion isn't an option because realistically the US doesn't have the resources to launch a large enough invasion against one of the largest armies in the world. The amount of effort it took to launch the D-Day invasion for example involved years of effort. And then the Nazis were forces to defend a long coastline while a lot of their troops were tied up in Eastern Europe and Russia. North Korea would only have to defend one side of their coast since they'd know quite quickly what side of the peninsula the US landing ships were on. The US could probably at most land a Brigade or two. Nothing compared to what is needed to invade North Korea.
The Nucs provide Kim with a great negotiating tool however the only problem is that China may decide that they don't want to have Korea controlling nukes right on their border and if China stops supporting North Korea, they're basically done. And China would have far less qualms about having a nuclear war with Kim and co.