I find it likely that the kids will spend their lives trying to live on their Dad's reputation.
I find it extremely unlikely that they will manage to parlay that into political power to any significant degree.
If the GOP truly has become the "Party of Trump" then the name alone would be enough to make any Trump scion a viable candidate.
Ivanka is a somewhat decent prospect for the GOP as she would allow them to claim that they're not misogynist, she's not actively stupid and she and Jared Kushner seem to have political ambitions.
Don Jr. could be viable in 20 years or so, as an older white man he'd appeal to the GOP base and by then the GOP and Trump family would be inexorably intertwined.
As Dubya showed, a wide range of personal and temperamental deficiencies isn't a barrier to being President so long as your family has enough pull in the party so there's hope for Eric yet - either that or he'll be a modern day Billy Carter.