No, she wasn't. Not morally, not ethically and not legally. She did not remove him from his home. She did not take him from his parents. The went for a walk and talked. She solicited his opinions and let him know that whatever his decision she would support him. His parents might not have liked that, they might not want their son to associate with specific groups or people. Guess what though, that's not illegal, parents throughout history complain about who their kids associate with and theres not much they can do about it unless they do something illegal (and spoiler, they didn't). Furthermore a part of her message was that even if he did go he was never more than a short walk away from his parents.
Two things, one spoiler, Kitty Pryde and probably many of the X-Men weren't abused. Two, Franklin's loss of powers could potentially be dangerous as no one understands the cause, and was the stated reason why the Krakoans got involved when they did. Unless of course you have actual evidence to the contrary...
Yes the group founded upon the idea of unity for all of their people wanted one of their people to join them, however its not just the Omegas. In fact there seems to be a whole half of the New Mutants that was dedicated to the idea of reaching out to mutants who didn't go to Krakoa and they didn't start with Franklin. The fact that they didn't approach until they learned about his power issues works against your thesis, especially as it could be a sign of harm inflicted upon him.
Further where has it ever been stated that they want the omega mutants for military purposes? That is either a gross assumption (which is an invalid criticism) or an outright lie (also an invalid criticism). In fact, we know of at least two omega level mutants who are kept away from military activity, Proteus and Hope. Unless of course you have actual evidence to the contrary...
Franklin is an un-emancipated minor and his parents have the final say on his care. However nothing in that means that others can't have an interest, advise, make recommendations and offer help. Schools and private institutions have been doing so for centuries. There is nothing unethical or immoral in that. Parents aren't required to take the help/advice but there is nothing evil, unethical or immoral about offering it.
Every person in the world has an agenda and no one invests in issues they are disinterested in. Xavier has spent his whole career being motivated by ensuring the well being of mutants. Franklin is a mutant in crisis because his powers are depleting and no one has been able to figure out how or why. The Krakoans have a significant amount of resources that even Reed Richards does not. Unless you have evidence that this was about something nefarious (You don't) your argument doesn't work.