You need to see a solicitor, make a will and specify who you want to be guardian of your children if you die.
However, even if you name your partner as the one to be guardian to your eldest, her father could still challenge it.
The Courts would take into account all the facts, including asking your daughter who she wants to live with.
Another alternative would be for your partner to legally adopt your eldest but I wonder if her father would agree to this.
If you make an appointment with a solicitor, ask intitally for the free 30 minute consultation.