Of course both of you think you are right, but this is a problem which
affects both of you and which has to be resolved one way or the other.
You may find that, when you have somebody neutral helping with the
negotiations, much of the heat is taken out of the situation. For
mediation to be successful you need to move
from entrenched positions to what is best for both of you. This is likely
to mean that you will both have to compromise.
But if you stick
with mediation you will save a lot of costs. I have known cases where we
had almost got agreement, but neither side would make the final move and
they resorted to lawyers whose fees were greater than the difference in
their positions when the mediation was abandoned. There's a lesson
there!
So, give it a go, listen to the other side, and be
prepared to compromise - and get a good mediator who can take control,
should the need arise.
I wish you well (both of you).