Q: I would like to ensure that my daughter's father cannot get custody if I die. How do I ensure this will not happen?

A: First of all you need to make sure that you do have legal custody as ordered by a court. Your summary above implies that you do but I am not 100% sure.

Second you need to set up an estate plan that plans for this contingency. As the biological parent the father may have better rights to take over parenting your daughter if you die but you can do your best to make a different outcome. To do this you need to talk to an estate planning attorney, preferably one who also has a very good understanding of family law. I happen to practice in both areas and there may be other attorneys that also practice in both areas but don't assume that all estate planning attorneys understand family law.

The right attorney will discuss with you a variety of things. There is no one easy fix. Through estate planning you can designate who will manage your money that you leave to your daughter so that there is no change that the father can get appointed to be her conservator. You can also set the age that your daughter get's any money to be older the age 18 if this done through careful estate planning. You don't have to be rich to do this. You can buy a life insurance policy and have the insurance fund a trust that someone other than the father manages. So the one thing you can do for sure is make sure that someone you trust controls the money, not the biological father. (There will still be social security that will be paid to the person raising your child based on you having died. There may or may not be a way to control that but you can at least fund a private trust with life insurance to make sure there is money to help your daughter.)

You will also do a designation of guardian which names who you want to raise your child. It is not automatic that the court will appoint a guardian over the biological father. But if you have someone in mind who would be better suited to raise your child and you can leave them money to pay the attorney fees for a battle with the father, they may have a chance of proving that the father is not capable of raising your daughter and win the right to be the guardians. Again, life insurance can be purchased to pay these attorney fees. In fact the trust mentioned above can be designed to receive life insurance for both purposes - to pay legal fees to keep your daughter from being raised by the biological father and to leave money to your daughter.

There are other possibilities. If you get married and your new husband is able to adopt your daughter, then the biological father would be eliminated as having parental rights. Similarly but not as effective, any adult that you have in your life that becomes like parent for your daughter can petition to have custody of your daughter using Oregon's psychological parent statute. ORS 109.119: https://www.oregonlaws.org/ors/109.119 What has to be over come is the father's constitutional right to raise his biological child that was established in the Troxel case (and ORS 109.119 is designed to deal with) Read Troxel: https://www.law.cornell.edu/supct/html/99-138.ZO.html

So there are things you can do and anything you do is better then doing nothing. See a lawyer.