Mija did like the other cat who died, right?, so it may not be impossible to find one she likes or will tolerate, and your sons could then have a cuddly kitty.
However, the life you describe doesn’t sound bad at all, with full house access during the day and only certain wings open to her at other times. Perhaps when she comes meowing for attention, she can be rewarded for that prosocial behavior by getting some attention from your husband, whom she likes, or you, whom she also likes, if a little less. Honestly, a little attention-seeking behavior can be seen as a good thing rather than a sign of desperate loneliness (so desperate you feel it is worth ending her life over. Is she losing weight? Listless? Anything besides just at certain times of day soliciting some attention?) Doesn’t really sound “depressed” or “lonely” to me, though she is probably adjusting to the loss of the other cat.
In the meantime, start building some positive associations in the kitty’s mind with your boys. If I’m understanding correctly, the younger is 3, so could the older one, perhaps with assistance (esp. if there are cans to open or heavy bags to lift), feed kitty? No touching or petting, but just being the one to fill the food bowl and put it down, with Mija present. Many cats make strong positive classical associations with the sound of a can opener or other signals of cat-food-preparation, so use those to make her think the presence of your boys is a good thing. Hopefully, all parties can enjoy that task and start to build positive associations with each other. And your boys can feel they have something to do with Mija even if it isn’t petting her. ETA: Ok, I re-read and see where your older DS is almost 7, right, so maybe that is indeed a workable plan to set up some positive interactions between kitty and son(s).
And in a year or two your sons will be older and she may be tolerating them better anyway when their gross and fine motor movements are more like an adult’s, and they may better understand what kind of touching kitty likes or at least tolerates.
And maybe the checkup to look for a spinal or pain issue, too.
Life really doesn’t sound that desperate for this kitty, from what you’ve described so far. And scratches kind of go with having cats, I think.