I saw both during both pgs. & both were totally fine with me being on Lovenox & baby aspirin. They had both dealt with plenty of patients on it & already had their protocols in terms of when to wean off close to delivery.
Doctors less familiar with it may freak out, but those who are familiar usually do not.
I actually had my water break early with ds #2 & was admitted to the hospital. They held off delivery for 24 hrs. b/c of the Lovenox. Nobody freaked & that was an unplanned event.
I would just see the peri. for your appt. & hopefully he or she will be better versed on the issue.
FWIW, I was a Beer Center patient & neither my peri. nor my ob/gyn were on board with much of it, but nevertheless, they were fine with the protocol.