Should I disclose my reason for wanting the position? How do I approach them...wait until the end of the experience to pop the big "will you write a letter" question, or accept the position with them knowing that's what you're working for.
I had loads of research experience but no private practice exposure and was strongly advised to get some before applying. So I had exactly the same situation when finding someone to shadow. You should state up-front that you're applying to veterinary school, you expect the experience gained while working for them will help you tremendously in your education and career, etc., and you hope that they would be willing to write you a letter of recommendation at the end of the summer. Try not to phrase it as "I don't really want to work here, but I need the letter, so..."
If they know up-front that this is a temporary gig for you and your ultimate goal is vet school, you will be less likely to end up in uncomfortable situations where they are trying to offer you a continuing position and you actually just want to get your letter and get out. And if they know up-front that you want a letter, then you'll avoid the uncomfortable situation of having worked your tail off to get a good letter without yet knowing whether they're willing to write you one.
Believe me, people expect this kind of thing. Just emphasize needing and wanting the *experience*, rather than needing and wanting the letter, and you should be OK.
(PS. I have ended up learning quite a lot while shadowing, and I'm actually still doing it once a week even though my applications are in and I have acceptances back. It hasn't changed my plans to *not* work in primary care private practice, but I believe that things I've learned about client interactions, small-business woes, and public perceptions will be applicable in some fashion down the line. So keep an open mind, try not to think of it as working *just* to get the letter, and absorb whatever lessons come your way this summer...)
