I don't think the guilt trip is necessary in this case.  There was a prior commitment that had to be honoured.  When we say we are going to pick up our kids, I would hope that that they would be able to depend on that, short of an unavoidable  delay.   It took me years but I eventually came to realize that I couldn't please everyone who approaches me.  If I am free, then I am glad to help, but if I have to be somewhere else, or take time to do something that I have promised to someone else, then I must say no, unless it is a matter of life and death, which it generally isn't.   Prioritizing the commitment I already have ensures that I don't let someone else down.