A few years ago I was working with a colleague who had previously had a more senior position than me. Partly through bad luck, partly through his own mistakes, he had ended up on a level with a less qualified person (me.) He tried to get back some authority by querying and criticising every decision I made. Where he was the decision maker, he expected me to follow his instructions without question, but where I was in charge he always tried to take over.
Eventually I decided exactly what to say to him (I even wrote it down beforehand, to help myself keep calm.) More or less, I said, "Jim, I've noticed that you're not happy with a lot of my decisions. Would you like to tell me more about how you think we should do things differently?"
This worked because he didn't really have a problem with anything I did, just with the fact that he was no longer the boss. After this there was no more niggling; if he really disagreed, he just said so, which was fine.
Eventually I decided exactly what to say to him (I even wrote it down beforehand, to help myself keep calm.) More or less, I said, "Jim, I've noticed that you're not happy with a lot of my decisions. Would you like to tell me more about how you think we should do things differently?"
This worked because he didn't really have a problem with anything I did, just with the fact that he was no longer the boss. After this there was no more niggling; if he really disagreed, he just said so, which was fine.