Stop giving into her. You are creating your own problem by telling her it's time to be done, and then deciding to continue. Of course she is going to throw a fit when you finally put your foot down and tell her no and mean it. She's come to expect that you will still cave. The more you give in to avoid a tantrum, the more likely she will continue to have them to get her way. Give her a warning of X more minutes, then stick with it. I see a lot of parents with kids at that age that expect the kids to just say "Okay!" the first time and understand why and just magically cooperate, but the thing is, they DON'T. Toddlers and preschoolers (and sometimes even into kindergarten) are very egotistical little beings and truly believe the world really does revolve around them. Their goal in life is to get as much out of you as they possibly can, and it's your job to put a lid on it.
You really, really need to set some boundaries and reasonable limits and stop feeling guilty about it. I have to tell my daughter no all the time - because I am tired, because it's getting late, because we need to get home, because I've had enough. And the more you do it, the more they will get used to it and learn they cannot push you around and manipulate you. And in the long run, they will be better people about it. My daughter, at 3 and 4, used to test me and the limits all the time. At 5, she still does sometimes, but not as badly, because she knows I mean business and I mean what I say. I look at it like, that's her job, and I have my job, which is to be the parent and be in charge.
As she gets older and goes to school, she will be expected to be done playing on the playground when recess is over and come in with the other kids. She will be expected to participate in whatever is taking place and be okay with moving from one activity to another. She will need to learn to respect the needs of others instead of just being focused on what she wants. It becomes easier as they move out of this egotistical stage of life but only if they start practicing self-control now. A great saying I heard somewhere was, "Don't let kids be in the driver's seat - they make lousy drivers."
Every kid needs to learn to live with "no."