So at what stage will DD2 be aware of her Father, if her sister is a full sibling or half a sibling? Are you saying your ex doesn't want to see DD1?
Yes it may have seemed wrong that things went ahead when DD1 was poorly. Your ex agrees on this situation. A contact order is a contact order, are you saying he's scared of his own mother, so took poorly DD1 to see her anyway?
Were the letters to you, trying to reason with you, or letters to the DC?
You will ultimately create a situation where the GM gets arrested, for nothing more than spite.
There's plenty of women on here, in the wider world too, that don't get on with their PIL. Most suck it up for the children, as they are important, they have a right to know their grandparents and other family, plus their identity.
You need to be careful with how you handle DD2, as this could cause damage, that 'could' make her ultimately resent you.
It's a bit like talking to a brick wall though, as you think your feelings are paramount, not those of your DC. The amount of women that dislike their PIL whilst DC are growing up, then get a great relationship when it's not about rules and boundaries, must be considerable.
Just an example, the woman who hated that her MIL spoilt the children, but when DC were older, had her children not biologically related to the ex MIL visit, as she realised it was love and care that drove the GM behaviours.