Lets see now ... if memory is right ...
British single mom with four kids, one girl OK, one boy clearly a chronic problem for her and to himself (it would seem) who won't even stay thrown out of the house, one 14 y.o. boy who seems bent on copying the older brother, one somewhat younger (12 or 13, depending) boy showing clear tendecies toward brothers' decisions. In all, as she views it, evident non-success with 3 of 4.
Also, no help from authorities, social services, police etc, whose best advice is don't bother us. Family doctor says 14 y.o. should have seen a shrink years ago, but has for years refused to refer him.
Toss in alleged total absence of private doctors - medical or psychiatric, no local programs to address issues (not talking send 'em away programs either). Suggestion made elsewhere to move was agreed almost immediately with viewing of potential new home (farm?) imminent [talk about moving quickly!!!]. So I guess money is there to move, but not to pay a private doc - when she got the energy to find one. Or was it the private doc couldn't make proper referrals.
So, now she wants help - a magic solution to overcome years of socially troubling behavior by her kids. However, that solution apparently can't involve them living apart from her.
1 of 4 is not a great track record, and there is no magic bullet to turn it around -- just as there is no magic program. Conclusion has to be she's looking for an ear and sympathy, but won't let go. I doubt she really could let one of her kids go to any residential program - no matter how wonderful -- or even a "regular" boarding school.
At a minimum, she needs the therapy, not the kids, though given their suffering including them in therapeutic services should help them and is the only hope for anything like "family".