Demand avoidance in PDA is primarily determined by the cumulative load of stress experienced by the PDAer. They experience all the usual causes of stress (for anyone) plus all the standard autistic stuff of struggling with changes of plan, lack of routines, social communication differences AND what is often a hair-trigger nervous system that goes into (negative) overdrive every time they perceive a loss of autonomy or loss of equality with others.
If you pick up a child and put them in the pushchair or car, they will experience an intense loss of autonomy (they don't get to choose whether to go in it or not) and an intense loss of equality (you are putting yourself "above" them in making them do something).
This means they will be dysregulated, which may involve meltdowns, self-harm, violence, eloping etc. They don't calm down and realise the avoidance wasn't necessary or justified. The demand avoidance is actually only the symptom, not the root of the problem. The problem is that their nervous system is telling them they're about to die, and the demand avoidance is their way of trying to protect themselves from a situation which makes them feel like that.
In future it is likely to involve further demand avoidance around going in the car / pushchair excuse they've learnt that it is an inherently unsafe activity.
It will also increase their cumulative stress load, which will increase demand avoidance for all other demands and particularly access to basic needs. So you "putting" them in the car may result in an inability to eat, to sleep, to clean teeth, to toilet themselves etc. When the cumulative stress levels and/or cumulative demands exceed their threshold of tolerance, this can result in PDA burnout which can involve months or years of being unable to do most basic things like eat, sleep, engage in personal hygiene, leave the house, engage in social interactions etc etc.
Helping a child to cope with the demand of leaving the house for an appointment requires a while-life multi-faceted approach which will include reducing other demands, using declarative language, making other language adaptations that help the child, working on non- verbal communication, offering opportunities for the child to experience autonomy and equality, understanding that demand avoidance is a nervous system reaction and disability rather than bad behaviour, working on emotional connection and building warm trusting relationships, and other strategies.
The best immediate way to help a PDA child do something difficult is to not require them to do it. Only when they have the legitimate option to say no can they stay regulated enough to be able to say yes.