Answering this or similar questions will be challenging for any worldview that takes into account second-order and long-run consequences of actions, not just negative utilitarianism.
Saving a child has many such effects that will be very difficult to account for: not just effects on loved ones but also effects on the ecosystem, climate change, demand for meat, the economy more generally, etc. So assessing the grief experienced by loved ones is probably only a small piece of the answer to your overall question. At the same time, it might be particularly salient or important because the bond is personal and irreplaceable. If this life is not saved, we can do little to offset that harm.
For what it’s worth, a negative utilitarian theory might also include the frustration of preferences in the evaluation of an action. To the extent that the child wants to continue living, this would provide reasons to save them, even by negative utilitarian lights. Whether this is a decisive reason is another matter of course.
If you do find negative utilitarianism or other suffering-focused views compelling, I think it makes more sense to ask the question: according to this view, what could be the very best thing I could be doing with my time and money? Most people who have asked this question have come up with interventions that seem much more impactful than saving lives directly -- regardless of whether the latter would overall be a good thing. Here is one person's attempt to answer this very difficult question: https://reducing-suffering.org/