I think it's reasonable for an EP to send their EAC a birthday card and a card at Christmas and the occasional loving message, if that's what they want to do. That is not IMO constantly hounding them. It's a way of reinforcing the fact that despite what they've done, you love them.
Not for me, almost 6 years now. Our ES doesn't want us in his life so we're not. We do send birthday and Christmas cards to our GC because for us, he doesn't have the right to deny his children their loving GP's, GGP's and large and loving extended family.
I agree agnurse that turning up at a GC's school or an EAC's place of work is unacceptable. If the GC knows their GP's and would recognise them, this could cause them a great deal of upset and confusion but if the GC has never met their GP and wouldn't know who that person standing near the schoool gate, hoping to catch a glimpse of their GC is, no harm is being done to the child.
You say you "get that estrangement is painful (you) are estranged from (your) sister". All estrangement is painful but I don't believe that the pain of estrangement from a sibling is the same as the pain of having your own child telling you they want nothing more to do with you and that you'll never be allowed to see your GC.
Harassment is against the law and now emotional abuse is also a criminal offence. There are many EAC guilty of the latter.