How can I politely tell Laura that Anna is feeling uncomfortable from such pressure and we (me and my partner) are not interested in creating the "big, happy family"?

Don't make it about Anna's feelings. Laura doesn't need to know them. Make it about your own feelings. If Laura needs to blame someone, she should blame you. It's your role to insulate Anna from Laura. Anna didn't sign up to start dating Laura when she started dating you.

As a father, it's also your role to make sure your ex doesn't use your kid as a weapon against your current girlfriend. What your ex did on Facebook was absolutely unacceptable. A kid shouldn't be put in an untenable position like that.

You say things are amicable, but from where I'm standing, you're the only one who seems to be amicable and overly nice. Anyone else would have shut down your ex in her manipulation attempts right away.

How can I politely tell Laura that Anna is feeling uncomfortable from such pressure and we (me and my partner) are not interested in creating the "big, happy family"?

Don't make it about Anna's feelings. Laura doesn't need to know them. Make it about your own feelings. If Laura needs to blame someone, she should blame you. It's your role to insulate Anna from Laura. Anna didn't sign up to start dating Laura when she started dating you.

As a father, it's also your role to make sure your ex doesn't use your kid as a weapon against your current girlfriend. What your ex did on Facebook was absolutely unacceptable. A kid shouldn't be put in an untenable position like that.

You say things are amicable, but from where I'm standing, you're the only one who seems to be amicable and overly accommodating. Anyone else would have shut down your ex in her manipulation attempts right away.