The question How can I mediate between my fighting adult siblings? to me seems like it should be closed.
What strategies can I employ to mend this relationship as a sibling?
To me this seems like a "what should I do?" question and I would vote to close as off topic. However the question has been edited by a moderator to bring it in line with on topic questions. Should I trust the moderators decision or vote to close on what I think of the question?
You should make your own judgement about whether or not a question is on topic and vote accordingly, regardless of whether a moderator interacted with the post.
Mod votes for closing, etc., take effect immediately, so we tend not to vote unless:
For this question, I saw that it had a couple close votes for being a "What should I do?" question -- but also that the sentence containing "Should I?" could be removed without really losing much. So, I went ahead and made the edit. My hope was that by removing those words, reviewers would be more careful about deciding whether or not it really was a "What should I do?" question at its core -- so thank you for that!
Even if a mod straight up says "I think this is a quality, on-topic question", you're always free to vote to close if you disagree. Stack Exchange sites are shaped by all users in their communities, and sometimes we'll have different ideas of what's on-topic and what's not. If the user you happen to disagree with is a mod, that's fine too! We're still human ;) If there's four others on your side and the question gets closed, the most likely result is that we'll ask for opinions in chat or make a meta post (like anyone can!), which will help everyone by setting a little more precedent and clarifying what we can agree is on topic and not.
Like Cashbee mentioned, mods frequently also edit to fix grammar, spelling, and formatting, without significantly changing the substance of the post. Sometimes we also copy-paste content from the OP's comments, so that the comment section can be cleaned up. So, just seeing that a mod was last to edit doesn't necessarily imply anything about the quality or on-topic-ness of the content - you can click on the edit history link on a post to see what exactly was changed and compare against the older versions, and decide for yourself.
You do not have to trust mods in that sense, no. You can always challenge the actions of mods, they are not dictators of this stack. You can vote and flag your own conscience, so if you feel like the mod's edit was not sufficient enough to make the question on topic, then go ahead and vote to close. In such a situation, make sure to leave a comment where you explain why you still think it needs to be closed.
In this instance, the mod that edited the question also left a comment behind, asking for more information. I have not yet read the question itself, but it seems even that moderator thinks that the question is not yet perfect.
As addendum, I once was in the very same situation as you are in now. I saw that a mod edited a question but I still voted to close. It turned out that the mod was only fixing grammatical errors and typos. I had a good laugh with the mod afterwards in chat. (You can always talk with our mods in chat, they are happy to explain their actions if you ask them. They are very friendly)
TL;DR
When a mod edits a question, that does not mean the question must be on topic afterwards!
