Anti-personnel landmines are triggered on pressure. They are designed to trigger on human stepping on them, not small animals like a dog, mouse, etc.
Anti-tank landmines are usually also triggered on pressure (and magnetic). They are adjusted to trigger on heavier vehicles only (as they are much more expensive than anti-personnel landmines). So an infantry with heavy equipment will not set them off.
And no army are so dumb to design the landmines to trigger on blasts so easily. Otherwise mine sweeping will be a very easy job. Just firing a explosive shell into the minesweeping area to clear all landmines? Such things never happen.
I don't know any design of real-world atomic/nuclear landmines. (Their design and deployment would be classified information, I am nowehre to get them.) But in common sense, I doubt if army will allow them to be so sensitive that they will be triggered by blasts. Some skirmish fights firing some explosive shells in the area will then set off all atomic landmines? No, I don't think any army will be so dumb to deploy such things on the battlefield. It does not worth it! Such sensitive landmines will set off by one or two of those flying shells, well before the target enemy tank formations even reach the area.
Guessing from my military knowledge. The primary use of atomic landmines are used to stop enemy tank formations, which are the most valuable targets they can get on land. So the trigger settings are going to be like anti-tank landmines, only triggered by pressure (and magnetic) of tanks, and won't be set off by just blasts.
Conclusion: By design, anti-personnel landmines are already the most sensitive in triggering. But even for that, blasts are not effective to set them off. I doubt atomic landmines would set off by blasts at all.
PS: Maybe they can be finely controlled by remote triggering too, but then they are no longer landmines. (They would then be called remote bombs or charges, which are out of the scope of this mod.)