Whoa. Slow down. I've posting in the Adoption Forum for five or six years. I'm a huge proponent of open adoption when it's safe and healthy for everyone involved. I've got two open adoptions. DS (and DD) was in his birth mother's wedding last summer. We've been to his half-sister's birth day party at his birth mother's apartment and to holiday get-togethers at his birth grandmother's house. We've got close relationships with both of his bio-sisters and their adoptive families. We recently met DD's bio-brothers and their pre-adoptive family. We have been to a park with them and were even invited to their house for Thanksgiving (but won't be attending.) Their being in foster care and being adopted has never been a secret. But, what that all means is something that clicks gradually for kids. It's not a "one-stop explain it all and everything's understood" kind of thing.
My kids have learned about adoption in an age-appropriate manner all along. DD's been in my home since she was a baby. She only had ONE visit with her birth father and that was right before the termination happened. She was a toddler. When we were in court for the TPR, I told him that I'd like to have contact once her adoption finalized. But, that the contact info that I was given (for a relative) must have changed and there was no way that I could get in touch. And for a while, he was back with her birth mother and that is a deal breaker for me for safety (and comfort) reasons.
I have stepped outside myself and thought about what he feels. I don't know how to further prove that. And I absolutely think about what DD feels now and might feel in the future. I spend hours talking about it with friends (IRL and online.) If I didn't feel it was important to my kids and their birth families, I wouldn't go to all of this trouble. But, the child's needs need to be primary.. He is a genetically-connected stranger right now. I can use the words "birth father" right now even though she doesn't know what that means. Growing in someone's tummy (or uterus) is one thing. It's physically obvious. Fatherhood is different.
We read books about adoption, talk about their adoptions, belong to two transracial adoptive parenting groups, and talk about people we know who are adopted. We are embracing the Hispanic side of DD's background. I help others to understand that some language surrounding adoption is hurtful, or confusing, to adopted kids. Like the whole "adopting a family for Christmas" or "adopting a child overseas." I encourage others to use the the term "sponsoring" instead of "adopting" because it's confusing to my, and other, kids. My kids know that we help babies who can't live with their families for some reason. They may not understand that we are a "foster family" but they do know that we are ready and waiting for an infant or toddler to join our family (for a while or forever) if it's needed.
You can't tell me that we don't talk about adoption.
This is not a stranger, this is her birth father. I would step outside yourself for a minute and examine how he feels. How you dd will feel later. Adoption should be talked about at an early age- much earlier then 4. Your dd does understand if you would explain it to her. She knows babys grow in tummy's. You can make it age appropriate but you do need to tell her.