Jon Penn's Answer:
I certainly sense your frustration and anger. It will be important not to let these build up, and potentially undermine your long years of good service to the organisation and your colleagues.
I am guessing that your local organisation is a fairly small one, and therefore maybe you don't have written policies or rules regarding criteria for time off, and equally no processes for grievances?
I am also wondering what the culture in your organisation is, and whether it has perhaps changed over your time there? And have you, as well? Could that be why you may be perceived as "too harsh"? You refer to "constantly being undermined by staff and your supervisor" and I assume this is relatively recently - just since the event a year ago. You don't say in what way, and I am guessing you feel it has gone well beyond the requesting time off issue that you do mention.
You referred to your 13 years' service, with no complaints; and again I am guessing that there is no regular appraisal system or systematic one-to-one sessions with your boss, and likewise you with your staff? So perhaps no feedback is all the feedback you get! You also mentioned your boss "polling" your staff about your abilities in your absence. Did you get any feedback on what they said? It strikes me they may well have been very complimentary about you! You are obviously very conscientious and keen to behave professionally and do a good job.
What is noticeably absent from your story is any comment about relationships or a sign of empathy between the people involved. I wonder if you see building such relationships as a key part of a managers' job?
So what to do?
First of all stay calm and make sure your frustration is not either distorting your view of reality or damaging relationships either with your staff or your supervisor, or worse still affecting your health or well-being.
Gather together some recent examples of issues, so you have some "facts" to refer to in conversations.
Then I would request a one-on-one meeting with your line manager to talk [not complain!] about your concerns i.e. them getting involved in what was your decision, rather than supporting your decision, or discussing it privately with you, and so making it difficult for you to manage your team; and also them polling your staff in your absence, but not giving you any feedback on the response.
I would phrase this meeting as you "asking for their help to allow you do your job well".
I would also suggest asking for regular one-on-one meetings in the future to improve the effectiveness of you and your supervisor, working as a team. You do need to be willing to ask for AND listen to constructive comments in these meetings!
Hopefully this might lead to confirmation that your boss does value your work, and they will agree to either support your decision, or at least discuss their concerns with you in private in future. I think you are entitled to hear the results of their "poll" of your staff, and I am sure that they will be positive.
If it doesn't lead to this Ė perhaps if they dispute your version of events, or simply feel their action was appropriate and justified, or give negative feedback as a result of their poll, you need to have thought through how you will handle that. If you don't already have one, I think requesting a detailed job description would be the place to start, and this would allow some conversations with your boss about what excellent performance looks like and how you are doing compared to that vision of excellence, and would show your desire to achieve that level of performance.
Unless there is some compelling reason not to, and almost regardless of all the above, I would start doing regular one-on-one sessions with your team members to build relationships and give them feedback, and as part of this, request advice from them about what you could do more of / less of / start doing / stop doing to make them more effective and happy. These sessions would settle down to be no more than 30 minutes every month or so, but will be invaluable use of time.
A final comment is to remember that a high performing team or organisation does at least two things really, really well. They have a clarity and obsession about their purpose; and the way they care for and look after each other. I was left wondering about the how the second of these works in your organisation?
So Good Luck. You have choices you can make about how to move this situation forward, and the key thing is to not let it fester and drag on!