Is nuclear the solution?
Not if time is of the essence. But let's say there is no time requirement. A Chernobyl-like "nuke" is relatively quickly build. Would you want such a plant near your home? 95% of residents in the US wouldn't want such a plant. The risk is there, and you'll rob money from many people by diminishing their property values over night.
Now, I will say that a "nuke" is great for base-load, but that could be countered with the fact that these plants are infamous for their slowness adjusting the amount of energy to put into the grid.
Nah, the real game is energy-efficiency. What can be done by spending the least amount of electrical/fossil/nuclear energy possible. So, for example: using a simplest, most direct way to cook your food. Why not use a a very insulated stove that you could power with 1 small solar panel? With enough thermal mass, such an oven would remain hot even during the night to cook something you fancy. No grid power, no battery, no nothing except patience and discipline.
You may get away with adding a lot of insulation to your boiler, in order to reduce its power demands so drastically you might get away with powering it via just a simple heat element and a small-ish solar panel. Barely any transfer losses, barely any losses to turn one form of energy into another. All powered by non-moving parts that require very little maintenance. And it is power the grid doesn't have to deliver to your home, meaning it doesn't need to be generated, or distributed.
And you'll slowly find ways to do that with the other things you deem essential.
Doing more with less in the household. Because that is under your direct control. And once you'll get the hang of this notion, you might think up solutions on a bigger scale. A scale that could be interesting to your employer, or your own business, if that is more your thing.
The climate wins and you win and, if you have any, your children win too. Manage to do so and you'll gain true independence, little by little.
From what I understand is that the average energy consumption from an normal US household is about twice the energy consumption of the average from the (Western-)Europe household, which in turn is about 3 times the energy-consumption of households in 2nd-world countries. Only mention this to inform you that there is a f.ckton to gain in becoming energy-efficient. And what all of the above doesn't need is another new "nuke".