Hotl you and I are in exactly the same position. The more I encourage, the less he is interested but will occassionally just disappear and then come out of the toilet to say he has done wee or poo.

I would bite the bullet and give it a try. I would chat to her about it, but not directly about her toileting needs. Something like mummy needs to go the loo before we leave because its a big drive. Then when you get to the shops, say mummy needs to go to the loo, pick the parents room that has the big loo and little loo in it. She may ask to go because she is in a different environment to home. Pack lots of clothes and perhaps a nappy just in case she wants it after an accident.
DD2 was very similar, the more we pushed things and talked to her about it, the more she rebelled. So in the end we just went round like normal, but I vocalised everything we were doing, did what I suggested above. Once she realised it wasnt really about her, but everyone needed to go out every now and again she started to open up to the idea.
Good luck though
This advice probably resonates the most with me. I have to talk to him about this, but not about going to the toilet.

I'm finishing work next week and we have a month off so will bite the bullet and see how we go.