7yr Granddaughter, how to handle separation anxiety with compassion and not be a martyr to it at the same time

Clearly very stressed and heading towards possible mental health problems if left with all these cant dos I think very gentle encouragement with a treat at the end doing something really grown up like a cake in a coffee shop after a walk or similar What about a visit to a cinema there’s lots of kids films out at the moment I think grandad should be involved abd she should go in the your car to learn that it’s safe and normal if you don’t take her in your car her phobia has won and she ll move on to the next worse one
The trouble is if you start allowing her troubles to take over you are encouraging her that the car is unsafe the cats can’t be left and the only safe place is her home then maybe her room and how many steps to agrophobia
She may need mental health help don’t be afraid to seek it out better than leaving this it will only get worse

I would walk with her, the exercise will also help with the constipation, take a bottle of plain water with you as she may also not be drinking enough. Has she got a dolly and a dolls pram to push? She could take dolly out for a walk to your house. She will be more relaxed about going home and would likely prefer to go home by car, breaking the psychological cycle about car journeys

I am sorry that her mum has Crohn`s

Bless her she is clearly stressed, but you have my sympathy. You are not too well and the prospect of being cooped up in a small house with a 7 year old is daunting. Chrons is a very distressing and debilitating condition and you GD may well have picked up on the anxiety that has enviably happened.
How about going to stay at your DD s but on the Saturday make it all about you ie " Don't know about you ' Sally' but I am a bit bored now and need a change, what can we do about that ?"
If the situation appears to be all about you rather than her refusal to go in your car or even out for a walk, it may take the pressure from her. Your GDs tummy issues are probably why she feels safer at home.
I suspect your GDs tummy problems all stem from her mum's diognosis and may take some time to be resolved. Alternatively once she is alone with you she may have a change of heart! I fully understand your worry about all this and I hope the weekend goes as well ( if not better! ) than you anticipated. Please let us know how you get on - good luck.

I’d just walk if she won’t go in the car hopefully she will change her mind.

Why not suggest walking, using a bus if possible or even a taxi!!!!
Travelling via a different method may spark her interest.😊

That's a tricky one, because obviously you can't just put her in your car against her will. I'm not bring facetious, but is there a bus nearby that you could go out for a ride somewhere instead? Or a train? It's less confined than a car.

Can your DH go with you, and help out, even if he returns home in the evening say, if you only live nearby?

Oh dear your poor GD and you. It does seem that she’s suffering from anxiety if she’s worried about a ten minute drive and then to say she doesn’t want to go in either car. If it’s a ten minute car drive is it too far to walk ?
I think depending how your feeling I would go with what your GD wants on this occasion. Maybe she’s worried about the tummy issues and feels more comfortable at home. You may find she’ll get bored and change her mind once she’s settled. Good luck.

Go with the flow. I'll bet that once her Mum and Dad are out of the way she might begin to feel more interested in going to yours - especially if you have something fun lined up - I am sure you can organise something that is worth 10 minutes in the car! - paddling pool?