The op is not about 'someone' who couldn't wait to use the loo, it's very specifically about a toddler. I think that changes normal rules and conventions. It sounds like the staff were going to be clearning up wee one way or the other, be it on the floor because he couldn't hold on any more or (more conveniently) in a paper cup.
The circumstances in the toilets have not been fully explained - I really don't understand how queues in a coffee shop could possibly be so bad, but the op did stress that they were. It's hard to imagine that the mother felt this was her only resource. But, I have found toilet queues are not sympathetic to panicking toddlers, and this is why I sympathise with her.
The bottom line is she had to do something. We don't have enough information about whether going outside was a valid option. I agree in most circumstances it would seem to be, but if not (e.g. it would take too long), then she had to do something.
I read from the op that the wee was left in the toilets, not the coffee shop itself, but as I said, the details of the facilities on offer are not clear.
Sure, I agree that just leaving it there sounds a bit urggh, but it also sounds like it was a very stressful situation for her and I'm not willing to judge her as being any of the things you've called her (and me for putting forward that view
) without knowing more details.
What would you have said if she poured it down a sink? Walked into the coffee shop with it? Or indeed, if you had witnesses a humiliated and distressed toddler wet himself and wee all over the floor while his mother just looked on aghast?
We don't have enough details about why she left it there - she could have felt utterly mortified and just fled as fast as she could, after having such an unsympathetic (why didn't anyone offer to help/ let her into a cubicle?) audience to her personal drama. It's unlikely it was a personal snub on the staff.
Unless I'm told that this is her regular way of getting her dc to wee in public (which I very much doubt), then my reaction remains sympathetic.