Hi. I'm drawing a US pension and live in the UK. It's fully taxable in the UK as foreign income, and would be regardless of the amount of the payment. The 401K is not taxable in either place until you take disbursements from it, I don't believe. Unless the pension plan states specifically that you are not eligible, if she has nominated you are her survivor, you should get the $50 a month when she passes away. Until then, I don't believe you are responsible for any tax on what she has disbursed to her.
Suggest you talk to the pension people to see how they want you to handle filling out the withholding form. (My assumption is that there will need to be a number of some sort assigned to you by the US govmt.) There are a few very tax-smart people on this board so I'm hoping someone will chime in here for you.
Your partner could request zero withholding, assuming she is a US citizen. If she is not, I believe they have to withhold 30%. (Same would go for you, once you become the payee on the pension or 401K.) Assuming also that she paid enough UK tax to take as a tax credit on her USA taxes, she should get all her withholding back for the tax year as a refund. She will have to file to get it. (Same for you, when that time comes.) The forms are not terribly difficult to fill out. She'll have to file with the IRS even with that tiny amount of US income, as she'll have to report all her world-wide income if she has US citizenship.
If you are not married or in a registered domestic relationship recognized in the USA I think she will have to file as "single". It shouldn't make much difference to the tax, as she'll almost assuredly be paying more tax in the UK than in the USA and will end up with a credit to carry forward. (AKA, she should get any withholding on the pension payments back in full.)
Again, hoping a tax wonk will chime in here to verify that. Good luck!