I'm not sure we have enough info. to be able to weigh in helpfully.
But in general, yes it does sound like the OP sides with the younger son. We can't know if we'd agree with that position or not at this point. However, that is a bit different than being "piggy in the middle," which, to me, implies being neutral.
I'm also not sure if "staying out of it" is necessarily the best way forward. For one thing, her feelings actually aren't neutral, which I'd doubt both sons aren't aware of.
Also, it depends on what the problem is. For example, what if one son did something terrible, even criminal, to the other. If I was the victim of that, I wouldn't feel supported or loved at all if my mother said she was going to "stay out of it." In other words, the terrible thing done to me was really nothing she was concerned about? Who needs family like that? I might respond by "staying out of" her life.
This is the kind of thing that can easily and permanently tear a family apart. Therefore, without any more information, I'd suggest involving a good therapist right away, if at all possible. See what they think of it and possibly then bring the brothers into it, with the goal of resolving the issue. Good luck with it.