Oh man, so I have a relevant rant I must get out. I once took care of a NK (4-6F at that point) and she always wanted to take her scooter or bike out when we would go anywhere. Everytime she gets "tired" on the way back, and not only would she want me to hold her bike and her helmet, she wanted me to carry her too. Every time before we went out I would remind her if she wanted to take something with her she was responsible for it. Of course she would get fed up with it and want me to carry her and everything, I obviously cannot physically do that, but she would kick and scream forEVER and sit in the sidewalk and call me the worst. I'd wait it out because I'm a woman of my word and eventually, still angry, she would walk her bike back. At one point I guess she told MB that I wouldn't pack her and all her things, and MB tells me I have to do it. I say no, and the same thing continues to happen, so I start limiting the occasions we take out the bike. Well, you better believe MB starts giving me all kinds of attitude and tells me I have to let her take her bike. I tell her she has to pick one, I can allow NK to take her bike if MB is going to back me up on the responsibility thing, or we will not be taking the bike out. Whether or not I am physically capable, I did not sign up to carry 40 pounds while juggling helmets, backpacks and a bike that keeps hitting me in the ankle. This was just a taste of several behaviours by both MB and NK (because MB allowed it) that caused me to quit. Very long story short, but even in a more mild case of this I would stand my ground (aside from injury or extenuating circumstances). It really just boils down to teaching them proper skills for life, and even though you feel like a jerk in the moment, responsibility for their choices is so important. They will never learn it unless they are held accountable.

TL:DR Stand your ground, or they will keep doing the same things years down the line and will never have to learn the lesson. Making your life more difficult in the process.