In my opinion, QOM, you should just go ahead with the date you've got, as you say Funeral Directors are busy and, to be honest, might not be able to offer you another close date.....as you say, you can't please everyone all the time and hopefully your Auntie and Cousin will understand.....the last thing you need now is aggravation and hassle just to please two relatives, and I will have no hesitation in keeping the date the Funeral Directors have kindly appointed for you and your Dad.
Hope all goes well for you, my lovely and I, again, pass on my condolences to you and all your family x