I was going to name change for this but what the hell.
OP I was a single mum with two sons at Eton. I did not come out of a wealthy marriage like you - I came out of a situation of financial and physical abuse and I never received a single penny for my DS from the day I left. I escaped with nothing except my clothes and the tools of my trade (musical instruments). No house, no car, no money, and a 'D'H who left the country and hid everything so I never got a penny, ever.
My DS were both at Eton on music scholarships. The school was extremely generous to me and gave my DS incredible opportunities beyond anything I could ever have done for them. I lived honestly, frugally, and worked hard to build up my confidence and my career again. I rented a tiny two bed house and let out the spare room to various lodgers. When my DS came home from Eton for short leaves and and long leaves they slept in sleeping bags on the sofas.
They did not have gadgets or clothes or phones or holidays (any, not foreign). I got very good at cooking with lentils. All our clothes came from Primark, and only when they got too small or worn out. The DS were not allowed to put stuff on the bill, and never did. No newspapers to the House. No trips.
They thrived. They were respected at school for their particular abilities, and nobody gave two hoots about what their home circumstances were. They never felt ashamed and did not hide the fact that their financial parameters were very different to many. Eton is in fact quite a mixed community. Perhaps being rich, you only mix with the rich ones. I can promise you that I was not the only mum at Eton who was completely and utterly on her uppers, and my DS were not the only ones who didn't have the things.
I'm not going to advise you on how to run your finances. But as someone who really does know what it means to be broke at Eton, I want to advise you to start being honest with your sons and with their house master. Because once you do that, you can stop faking it, and start making some rational decisions about how to sort out your personal and financial life.
By the way, ten years later, I'm totally sorted personally and my DS are both doing amazingly. But it starts with a bit of integrity.