I’m not suggesting that the house is the kid’s inheritance in the legal sense. But IMHO there is a substantial difference between an 8 year old whose parents get divorced (where there is a process of determining who gets what, who educates kid, who pays child support, who worries about the kids financial future) vs. a death where the kid is left motherless at a young age.
We don’t get to ask the late mom what her intentions were. But if the OP puts on her empathy glasses, I’m willing to bet she’d realize that the mom surely intended that whatever equity existed in the home would at some point benefit the D- whether she was living in the house when it was sold or not.
Blended families are complicated. But the family home (which the father left in order to form a new family with the OP and her kids) doesn’t seem terribly complicated to me. It was purchased with the late wife. It hardly seems like a joint asset with the second wife to be used for the benefit of the entire family, unless second wife had wanted to live in it, with her kids. Which for whatever reason, she did not want to do.