Thanks for all the feedback.
In my case, I came into my kids' life when they were already teens - son was 13, daughter was 16. They're now 19 and 22 respectively, both recently moved back into the house.
Their bio father is not at all in their lives and really never has been. So in my case, it hasn't really been a situation where I have to compete with a real person as a head of household, or deal with non-custodial parental interference. Maybe worse, I compete against what they imagine their bio father must be like.
It's mainly been a situation where they were alone with their mother like the three musketeers for so long, and I came into their lives at such a late stage, after they were already in their turbulent (and rebellious) teens, that they've been extremely resistant to accepting someone else in their lives in a parental role.
Early on, they seemed to make an effort to include me into the three musketeers, but that pretty much lasted until the first or second time that I acted more like a father than a peer. JBama, I remember the first time I got the "You're not my father!" treatment. Can't tell you how much that hurt.
They never warmed toward me enough to come to me about things - always run to their mother. She's been good about trying to redirect them to me, but they never would, even though I always tried to let them know that I was interested in their lives.
And here lately, since they moved out for awhile and got a little independence and confidence, then floundered (as young people often do, myself included) and moved back in, they've been almost downright disdainful toward me, as opposed to simply disrespectful, even though they're living under my roof and I'm paying their bills.
I guess I just feel very unappreciated and unaccepted by the rest of the family, in my own home (that I provide). Like it's mainly them - the three of them, and then there's me. And I'm not sure if there even is a way to fix it, much less how.