Thank you for all of your helpful responses to my post! Sorry I've taken so long to post an update, but a lot has happened in the interim.
After I made the original post and read some of your responses, I was planning on removing myself somewhat from the organization and asking one of my coworkers to take one of my workdays off of my hands. On the day I intended to ask her, she told me first that she was putting in her notice and leaving entirely to work for her family business. Crap! ... I'm happy for her new endeavors, but that left me as the only animal care worker Monday through Saturday (our one Sunday employee remained.) I suspected that the Founder and Board would not be very efficient in hiring new help and would ask me to cover even more days until they found someone (when I had intended to work even less.) I was definitely not prepared to work six days a week and deal with the trouble that would bring, so I had three choices: Run, and leave them with no staff to care for the animals, except the Sunday person. Brace myself and wait out the chaos, helping as much as I could and seeing what would play out. Or I could lean in and help them fix the core problems within the organization, ultimately making it a better place for me to work and better overall for staff, volunteers, and the animals. ... I chose to lean in.
It has not been an easy few weeks. The same day that my coworker told me she was leaving, I drafted a proposal for the Board to make me the Animal Care Manager, along with a list of some other structural changes within the organization to improve communications. Three of the six board members have been incredibly supportive; most of my suggestions have been approved. The founder is still difficult to deal with, but I learned that she is struggling with the onset of what is likely alzheimer's and is still in denial about it, which explains her mood changes; what often seems like apathy is really just the start of her memory failing. Only I and the board members know about this, which is why there is still so much hostility between the founder and the rest of the organization. I've begun taking on some of her responsibilities, and I think she's grateful, but it's very hard for her too. Now that I know the truth underlying her behavior, it's much easier for me to approach her with compassion.
As for my time commitment, I'm still able to work part-time. Starting on Monday, I'll officially begin my work as manager and will work in person at the shelter Monday through Friday 6-9:30am to take care of the new and sick animals, handling medications, special diets, inventory, and overall making sure all of our animals are doing well. (I'm a morning person so these hours are perfect for me! And it allows me the rest of the day for family time! I also made it clear that travel is important for my family, so we will be gone several weeks throughout the year, during which time the board would need to help cover - they were fine with this as several of them travel often and understand!) I'll have some work-from-home hours organizing animal records, maintaining the website, making vet calls, and helping the board hire new staff for the basic cleaning and care work. I've worked very hard to create rapport and build a positive relationship with much of our volunteer force, so they're ready to help us cover extra work while we're short-staffed.
I was so conflicted because, deep down, it just didn't feel right for me to give up on this organization yet. It's the only animal shelter for many miles, surrounded by corn fields and small industrial towns. I grew up around here and know that "animal welfare" is not part of the vernacular; this shelter is a one-of-a-kind place. I'm so grateful that my efforts are already having a tangible positive impact! It's definitely more work than I wanted to take on after early retirement, but I don't resent it, and my husband and kids are supportive (they've helped scoop litter boxes several times already, and my kids are always eager to love on the kitties.)
This experience has been so good for my personal growth too. It feels so different to work hard for something because I really care, rather than for the money. And this has certainly been hard work (physically, mentally, and emotionally.) There are still a handful of negative, grumpy people around, but they are now a part of my mindfulness practice, rather than a thorn in my side (most of the time - haha.) I'm feeling a lot more positive and grateful lately simply by working so hard to spread positivity and gratitude to others.
I have several difficult weeks ahead of me as I help the board hire new staff, get them trained, and acclimate to my new managerial responsibilities. I see an upward trajectory though, not without its battles (only half the board really trusts me yet), but I'm taking things one day and one situation at a time.
Thanks again for your support and advice! Mustachians unite to make positive change in the world - haha!