communion/bar mitzvah or any other such religeous events
Most people don't have these.
birthdays (every year as kids big ones as adults)
OP has said birthdays will be done separately, there is quite a big age gap here, and I don't think adults are likely to be too bothered about having two family members with the same first name at their birthday party.
graduation party
Don't know anyone who had one of these.
engagement party
Don't know anyone who had one of these either.
wedding
How much time do you think an adult is going to spend worrying about this on their wedding day?
having babies and baby related events (christening/baptism/naming ceremonies, birthdays)
If the OP's sons ever have children, which they may not, it's unlikely to be for another 20 years. And even if they do have children, they may, like most people, decide not to make it into a gigantic circus involving multiple events attended by all the extended family.
if they ever get seriously ill or injured and are in hospital
Yes, if I were hospitalised following a serious illness or injury, the embarrassment of having two half sisters with the same name who might coincidentally show up at the same time during visiting hours and cause a doctor or nurse to remark on the fact that they have the same first name would definitely be my biggest worry.
support during loved ones funerals etc...
Whose funeral do you imagine both these children are likely to attend, other than - God forbid - one of the OP's sons?
The OP's new baby girl isn't likely to be attending the OP's ex husband or his new wife's funeral, and the OP's ex husband's baby girl isn't likely to attend the OP's or her husband's funeral.
So it's really only likely to arise if the funeral is for one of the half brothers they have in common. In which case the one who has sadly died isn't going to care about his two half sisters having the same name, and the one who is still alive is going to have bigger stuff to deal with.
Honestly, these examples are completely mad.