Thank you for your question. My name is***** I have been a small animal veterinarian for 14 years and I'd like to help with your question.
So, it sounds like your dog has received vaccines for most of her life and it is just the last 2 years that she has not been vaccinated correct? The majority of the things that the vaccines protect against (most importantly, parvo virus) have immunity that last well beyond the expiration of the vaccine. And the older they are, the more vaccines that they have received over their life, the more true this is.
So, I don't think you have anything to fear from your older girl not being vaccinated. There are some things that she could give to the puppy... some intestinal parasites or kennel cough.... but I think that is very unlikely and wouldn't be prevented by having vaccinated her anyway.
I hope that helps, but if you have more questions let me know. If not, please don't forget to rate my answer. Best wishes!
Good luck with your puppy!