Yes we've had 6 years of this. Any time we have to get her from home mum will sabotage, she is happy to make our child completely hysterical if it suits her purposes. The only way we have found that consistently stops it is picking SD up from school. She's had hours away from mum then and can't see her absurd influence and hysteria and so she couldn't be more overjoyed to come.
We had recently a whole day of this absurd hysterics drummed up by mum, mum refused contact in the end that day. Finally OH managed to get to his child, within 3 mins of reminding her we were going to go to a treat, SD is in the car, chatting joyfully, couldn't shut her up. Ironically all the messing meant she missed the treat anyway, but didn't care, she was happy the whole visit.
We have a similar problem where mum is trying to demand back to court because of the 'distress' based on this one incident. OH pointed out that she never wants to come back either but that doesn't mean we keep her! And she has been upset going back the other day before!
I would therefore back up the poster who wisely says that even carrying the child, the upset was gone in minutes. Their memories are short at this age and they really don't know their minds sufficiently beyond immediate reward such as doing a fun activity they like, so I would just use the fun activity route. it doesn't have to be something like going out it can be as simple as the trip before promising hey we will make cupcakes next time, don't forget! Then remind them at the door, awwww but we are making cupcakes look at the blue icing I got, come and help me!
It's such total crap because their mum's cant' possibly conceive of the importance of just even sitting in a room with dad having a cuddle for an hour is actually more emotionally rewarding to a kid then a party, honestly I've seen it. I agree once you get the child in the car stop down the road and take a happy selfie, write a diary, video some whacky thing, anything to show the upset is completely temporary. We have had our child not wanting to come and crying a little, then 24 hours later in complete FLOODS of tears that they didn't want to leave one of our friends homes, honestly what 6 year old doesn't do things like that! It's INSANE to use it as an excuse not to do something vital in their life like have contact with their dad. If you set the life of a 6 year od based on their tears you would have them living in a friends cupboard eating nothing but jellybeans wearing a batman suit! A little sense of proportion please mums!!!!!! Of course for an obsessively possessive mum they LEAP on that just because its the one thing they want to hear. Very damaging.
If at all possible get a pickup from a place that's not mums, like direct from school. I assure you it'll be problem solved. Good luck.