I'm glad it looks like the dairy experience might come off. With regards to lambing, yes, ask around however I know from our own experience at home that dp works single handed and doesn't have the time to train someone.
I know you're a way from an agricultural college but it might be worth travelling to do one of their lambing courses - it could help reassure a stressed farmer that she's a safe pair of hands.
I take it she knows that the Royal Veterinary College are doing the NFU farm open days in June - it could be a good opportunity to show up, look keen and ask lots of questions.
As a vet the easiest and actually most useful experience prospective students can get is lambing in the spring. I would be writing to just about every open farm with in a reasonable distance to see of they have lambing space for next spring. Lambing is viewed really well by the colleges as it is a good exposure to how 24/7 the job can sometimes be. Dairy can be really hard to get as it is now much larger farms. Large animal vet experience even more so even actual vet students are struggling to get large animal experience. The most recent student I have helped get in had three years of volunteering in our clinic, two weeks on a beef farm (much easier to get) and 4 weeks lambing experience. No dairy at all.