I received this answer
From Gershon Eliyahu
Giorgies E. Kepipesiom
«For that matter, bonay is equally troublesome, as the children are not legally his sons, they are the adon's property, they have no yichus to the eved ivri, for example, if he later dies leaving no other children alive, these do not exempt his lawful wife from yibbum or chalitza.
My guess: the key word is "ahavti". True, she is not his, and not his wife. But he has fallen in love with this woman and these children. He is using the possessive forms ishti, bonay, in the sense of "I love this woman as if she were my wife, I love these children as if they were my own sons.
I said "this makes sense to me" and I received GEK's permission to share.