@Andrea5497 I hope all goes well with your pup's operation and wish him a speedy recovery!
Alas, this situation is not what is considered an extenuating circumstance in terms of your contract. You weren't unreasonable to request the date change, but I also don't think the property manager was unreasonable to decline it. Nothing in your agreement obliges them to be flexible on the dates if they prefer not to.
What would seem inappropriate to me would be to push the matter any further after a request has been declined. Even if you prefer a different outcome, no means no. So at this point, it's best to put aside the hard feelings and decide on a plan B. The choices are:
a) Keep the booking as-is but ask to change the check-in date to Wednesday
b) Keep the booking as-is but request to extend it to the following Wednesday or Thursday
c) Cancel the entire stay for whatever partial refund the host's cancellation policy entitles you to