If I were you I'd adhere to the words in her texts, so if she said:
"I'm only allowed to see the baby once a week."
Only let her see the baby once a week, explain that you'd hate to make a liar of her and as she said it was just 1 visit per 7 days, that's what it will be.
If she said "You never let me have any alone time with DGS."
Again, agree with her. Quote her words back to her and say "We did let you have alone time with him, but now us doing so would make you a liar, so we won't anymore, for your sake."
Etc.
The texts she sent are manipulated and abusive and they're lies.
By adhering to them, she can hardly complain can she?
If she texts, "can I come round and see DGS tomorrow?"
Feel free to respond with "No, because you saw him yesterday and as per your previous texts, you only see him once a week."
If she wants to admit she was lying, let her and decide how to love on from there.
But the bond of trust is gone now due to her behaviour, so she needs to feel that loss before she will change.