"The school would never use that word," Gosselin, 35, tells PEOPLE. "[Collin and Alexis] were not expelled. [The school] did not feel like they could meet their needs anymore, so it was decided they should leave, for now."
Collin and Alexis, both 6, are both seeing a private tutor who teaches them an "identical curriculum" until they are ready to return to school. But for now, Gosselin says the challenges are not just academic – they're personal.
"They've been the ones to verbalize the most that they miss Daddy," she says. "I could see that they're the ones struggling the most."
The Kate Plus Eight star says Collin and Alexis are seeing a therapist and "doing much, much better." They are suffering from post-divorce anger, she says, and were acting out in school in response.
"[Collin] was upset and saying things out of frustration – he'd crumple his papers and throw them on the floor," she says. "Alexis was angry in a different way. She didn't want to sit still. She'd get up and want to run around."
As for the rest of the Gosselin gang – which includes the other four sextuplets, Hannah, Leah, Aaden and Joel, and twins, Cara and Mady, both 10 – the reality star says she's just concentrating on being a good mom.
"I've kept the stability, the income – everything that they know and love – "I've come through on that," she says. "I am doing what my kids need me to do. That's really all that matters."