The US supplies the nuclear weapons systems and it's widely believed that they retain at least some operational control over them. As they do over many of the military systems they sell to allies, to be fair

Our subs are built by BAE systems and Rolls Royce. The missiles are built by Lockheed Martin. The missiles are fired from the sub. I wouldn’t buy a tv from someone who kept the remote in their back pocket.

Yes, I know all that. I used to work on software used in the sub design. What I wrote stands.

If that is true, perhaps we ought to start building our own! Doesn’t sit well with me.

To an extent it's not 100% relevant whether the US maintains technical or operational control anyway. They have total and absolute political control, unless and until the US leaves NATO and declares war on us. There's zero chance of us deploying nuclear weapons without their permission/orders.

I suspect if Trump manages to cling on to power for a full term the world, and NATO may look a bit different. We ought to be preparing for that, and we probably are.