To try to prevent my carsick child from being taken on unnecessary long journeys?

[AmIReadingThisCorrectly]

I would really appreciate peoples' honesty and also any solutions if you can think of any!

DD (2.5) has recently (within the last few weeks) started getting carsick if she goes on journeys lasting more than about half an hour. I don't think she really knows what's going on because she's just sick without any warning - she can't tell us it's going to happen :(
Anyway, DH has a son from a previous marriage who he collects on a certain day each week and then drives home 2 days later. We have him 3 days each week. Our jobs are totally inflexible when it comes to changing working hours so our days with DSS are always the same.
DH came home today and said that DSS' mum has asked if we can have him for an extra 2 days in a couple of weeks' time as she has a medical appointment, he said yes, this wasn't a problem. However, I'll be working on the day that DH will then be picking DSS up and therefore will need to take DD with him on a 1.5 hour round trip to collect DSS. There's a couple of dogs at DSS' house who she's scared of and DH's ex won't shut them into another room if we're there so having a break out of the car in DH's ex's house isn't an option. I really don't want DD to be taken on a journey which I'm pretty sure will make her sick but DH's ex isn't budging at all and is insisting that DH does the pick-up on the amended day. We don't have anyone who could look after DD if DH went alone to get DSS.
Is it totally U to insist that DH's ex drops DSS off on this occasion? I feel awful and that the situation is forcing DH to put one child above the other but I just really don't want to knowingly cause DD to be sick :(

If there's one thing I really resent about my childhood (one!) it's being carsick and no-one giving much of a flip about it.

I can't read a map or send a text (as a passenger) obvs to this day without feeling nauseous - but like most things, people who don't get it can't understand or imagine how miserable it makes you feel. My memories of holidays and trips out consist of me being sick.

For sicky dd,

Have one toy to cuddle in the car.
No books or toys or other things to make her look around inside the car.

Give her a sippy of water/juice (small)
And a few biscuits/crackers (assuming no choke hazard)

Play I-spy, with things outside the car, use colours or sizes for a youngster.

Eg something blue (lorry)

Have a quick break 5 minutes before getting to dss house.

Or let her sleep in the car, if it is anywhere near sleep time.

And keep the car cool.

Use air on, and don't over-dress her.

Hope one of those helps.

Car sickness is every bit as bad as severe pregnancy sickness.
Why would anyone inflict that on a child if it wasn't absolutely necessary?
The ex should bring their DS to his dad's home the evening before her appointment. Anything else would be totally unreasonable.