Without knowing the full story and not knowing what your staff are like, I'll will just comment on my experience. It is not always the staffs fault. Sometimes workloads can get out of hand and a good manager knows that that any work is not beneath them. In the end it benefits the business for the work to be done. Also as a manager you should be looking at workloads and making sure your staff are sufficiently trained to do it. On the other hand I have seen many lazy ***** that don't deserve a job. In this case rather than bitch about it take some steps to rectify it. Do monthly Performance Assessment set them goals and identity needs for training. Show them that it is for their benefit to. This way you weed out the ones who do not meet standards. This is basic management skills. Ones maybe you need to be reminded of.

you don't sound like the best manager to work with

You can't please everyone. Sad truth sometimes.

this seems to be a common thing with majority of the jobs anyone works these days.

It depends on what they mean by "do their jobs." A good manager should know and offer when their subordinate needs a hand getting something done. Not every day by any means, but everyone can get overwhelmed occasionally and a good manager should help them get it under control when that happens. Even by completing a task for them.

Not sure what type or business you work in, but by "do their jobs for them" are they expecting you to check out people at the register when their are only three people in the store, everything else is in order, and the employee just wants their 14th smoke break, or are they hoping you'll take over the register for a couple minutes while there's a line ten people long, while six people are waiting for help finding something, and half the shelves need to be restocked, the store is understaffed because you scheduled for a Wednesday at 9 am, despite it actually being a Saturday and the first day of a sale, and meanwhile you're just standing around "overseeing" rather than helping make things go more smoothly. I've never been a manager, only a hostess and a cashier, but I've worked around some lazy a-holes who wanted everyone to do their job for them. Usually there are only a couple to a team, otherwise nothing gets done, and they almost never complain about others not picking up the slack to higher ups because they don't want to draw attention to their laziness. I've also had times where I had to help do other people's jobs, or had to have someone help me with mine, because we were simply too busy for the number of people working to cover it all, and so those who had a free moment used it to help others catch up, that way everything worked better. At times like that the people who just do what's in their job description, and not a letter more, are just as bad as the lazy a-holes. The fact that enough people complained that your boss mentioned it makes me wonder if they had a point. The fact that the other manager only does the extra work "sometimes" means there was probably a pretty good reason for why she's doing it, and that she's not just overly generous.

Ask to see a copy of your job description. Then ask them to point out where it says you have to do other people's jobs for them.