Are you heterozygous or homozygous for Factor V? Have you ever had a
blood clot?

If you are heterozygous with no history of clots, it is controversial
whether you need anticoagulation.

There is also a difference whether you need full anticoagulation or
just coagulation prophylaxis. The latter, with lower doses of heparin,
is not always considered a contraindication to epidural anasthesia.

Often times, we discontinue heparin during labor anyway (then restart
it after the baby is born). Regular heparin has a short half-life and
can be timed so it wears off in time for an epidural.

There are a lot of factors and decision points in your care that seem
to be glossed over here. I wonder if either your provider is not
totally aware of all these complexities, or whether he/she has done a
poor job of explaining them to you. In either case, I think you might
benefit from a consultation with a perinatologist. If you are going to
be on heparin therapy, it would also be good to have an anasthesia
consult before the time of labor so that the plans and questions are
addressed ahead of time. You don't want any "surprises" at the last
minute, and you certainly don't want your option of an epidural closed
off because of a miscommunication or misunderstanding.