At the moment it all sounds pretty normal to me, she has a grandchild who she obviously loves, you and she clearly have a normal relationship in that you are both acting like adults etc- the thing that seems awry to me is the aunt's interferance- I would be careful of her- she sounds as though she's stirrign the pot due to a hidden agenda of her own.
I'd just carry on as you are if I were you and see what happens, as she has no automatic rights whether your ex is named on the birth certificate or not- and whether he is, is entirely up to you two, lots of people have only one parent named on theirs for all sorts of reasons, so don't worry just enjoy your child and continue to let him and encourage him to have a good relationship with his grandmother, you are doing absolutely the right thing.