Runs away from me when it is time to leave
Before You Begin
Pause and breathe. Even if this shouldn't be happening... accept that it is and embrace it with composure and calmness.
Calmness is the only way forward because without calm, there is no possibility for receptiveness and connection. Your child won't give to you any more than they see from you.
Never forget that a strong connection is fundamental, as there will be no correction in them if there is no connection with you.
The Core Problem
The child does not have perspective on why they need to do what you are asking, and is enjoying the attention from you.
What Will Make It Worse
Chasing the child around or becoming overly frustrated will not bring an end to these power struggles, or change their perspective on the situation. It will only embarrass you and make you feel resentful towards them.
What The Child Needs
1. To see that you understand what they want: Encourage the child to communicate what they would like to do verbally, instead of running away. Patiently listening to them, using active listening so they can see that their wants are something you care about.
2. To understand the distinction between you not wanting them to be happy vs. you abiding by the the needs of the day: Help them see that the needs of the day are what is putting an end to this activity, because there is something important that you two need to go do that has consequences for the family if it doesn't happen. It is not that you just want them to stop to be mean to them.
3. A part in determining when they can go back to doing what they were enjoying: To show you want them to enjoy themselves as often as possible, empower them to figure out when the next time they can continue this activity is. Praise them for "helping to find a solution to this problem."
4. Regular connection and attention: Ensure that the child is receiving positive attention and connection during the day to reduce the desire to get attention through negative behaviors.
How To Have The Conversation With Your Child
This conversation can happen in the moment as long as you are able to set aside your frustration, and oftentimes embarrassment, and maintain your composure. If that isn't possible, you can adapt it for having later that day at a time where everyone is more relaxed and they aren't distracted.
Speaking in a calm, lower volume voice, express that you can see that they don't want to leave. Ask them to explain why they don't want to leave, and repeat back the main reasons to them so that they can tell you listened and care. If their body language is giving cues that they don't want to go (e.g. sad face, clenched first, a difference in tone from their normal voice) then mention to them each of these things using the script "I can tell how important this is to you, your _[insert cue 1]_ and your _[insert cue 2]_..." [This is "What The Child Needs" Step 1 from above]
Then do Step 2 by explaining to them the reason, outside of your control, that you and the child have to leave, really emphasizing that it's also a bummer for you that it's time to leave.
Close with Step 3 where you show you're on their side you by asking them to think of the soonest time you can return (if applicable). The empowerment you are giving them, in combination with looking ahead to the next time, will shift the child from defeat today to something to look forward to in the future - an important perspective change that helps lock in their cooperation.
The 4th step listed is very helpful in significantly reducing this and other bad behaviors because the more time the spend with you bonding and enjoying themselves, the more they won't want to do something to stop that as a consequence of their bad behavior. In a sense, if they have fun time with you to lose they will be more likely to go along with something they don't want, but if they have nothing to lose then they will do what they want and take whatever kind of attention they are getting.