I couldn't not respond after reading this, you sound so worn down and desperate.
What I will say is that you sound the most wonderful mother. Completely get the guilt thing, my best friend told me when I was pregnant that it's not something that ever really goes, you will always feel guilty about something or other, part of being a parent! The other day I was cutting my sons fingernails and I caught his skin accidentally, it bled and he cried. I felt awful, I had caused pain to my son. In the same way, You must try and begin to look past the vaccine thing, it cannot be changed and it will tear you apart googling it and thinking about it all the time.
You cannot be a perfect human and a perfect mother, we will do things wrong, have days when we feel we cannot cope, want to run away, mourn our old life and freedom. But I can absolutely say that your children are better with you. You say that your daughter is the happiest little girl. That's because of you, you have shaped her, you have raised her. You are her entire world and you are good enough!! You must try to believe it!
How were you when your son was little? How are your circumstances different? Is there anything that helped you back then? You say that your husband is away a lot and he doesn't sound that supportive, trust me that will play a huge part in how you are feeling, the enormity of doing it on your own. Is there no other sources of support you can access?
Oh and please don't feel guilty about the formula. It will enable you to leave DD for a little bit and have a break, it sounds like it's what you need! The first time I left my little boy it was for a hen do, I felt so incredibly guilty (there's that mum guilt again!) it seemed I was going for a selfish reason and as it wasn't for his benefit I felt awful! I panicked about breastfeeding, would he eat, would he sleep?! But when I was there, I felt like the old me for a little while, I didn't have to worry about the things that utterly consume me day to day. And I came back refreshed. Baby was fine!
Please speak to your doctor. Tell the receptionists you don't want to discuss it. You just sound worn out and need a break, not a new life. Keep writing on here.
All the love in the word to you 