Clever girl!

Most of the parents rooms now have a big toilet and little toilet for the kids. If I take DS2 to the normal ladies toilet, I just hold onto him or make sure he is holding onto the sides.
You can get the training pants in various sizes...I assume you are talking about the Huggies ones's with wetness liner? They are only designed for accidents, so I would use a pull up at a play centre as that is the time when he would be the most distracted and just forget Lol.
I would just carry an extra set of clothes with me (including socks and shoes).