Sorry, I am a little confused, can I clarify please:
Who is ‘she’? The mother of your current partner’s children?
Are you also saying that ‘my ex’ - the father of your first daughter - also doesn’t like the idea of ingratiating your daughter with your current partner and his children? Or have I got that wrong?
How does the biological mother of your partner’s children know you have depression and anxiety? Is it because she gained access to comments etc you expressed on social media?
Social media is not private as you have put the information out into the public domain. It only becomes ‘private’ so to speak, if a person has gained access to your account without your knowledge or permission.
Is there any specific reasons you know of which could have lead her to believe that you are unfit to be around these children? I am not suggesting she is correct or not but please be honest. I’m guessing you wrote certain things on your social media accounts that perhaps weren’t your finest moments?
As far as I am aware, unless you have any criminal convictions against you regarding domestic violence and/or domestic abuse, you are legally allowed to be around the children.
But, it sounds like a bit of a grey area so I would take the legal advice you have been given as its customised to your specific situations.
I’m sure I don’t need to say this, but social media is not a good place to air your grievances... as you have found out, people can and do use it against you. Diaries are better in some ways as at least you can tear out pages and burn them should you change your mind 👍🏼