I'm really sorry you're in this situation. It can be hard when children aren't invited to parties. But, as you mentioned you haven't invited this boy-or anyone else-to a party before (since your son was 4 years old even!).
As others have said, invitations are often reciprocated, unless the children are very close friends, which it seems may not be the case anymore.
It's a bit surprising that the other mum signed her son up for an activity without being able to get him there or back. Personally, I've often given lifts to and from activities, not always expecting a lift in return. I do it if it helps the child, especially if they live nearby.
I try to remember that any issues I have are with the parent, not the child, so I don't want the child to miss out because of that. But I'd not want to be tied down to doing it ALL the time, so just be clear about what you're prepared to do, even if that means a 'no' to all lifts.
Also, it's important to keep an eye on our own feelings when our kids are left out. In my experience (and I know this can vary), boys often don't worry as much about not being invited-at least, my three sons haven't felt left out in these situations.
Was it your son who was upset, or did you feel upset on his behalf? There is abig difference. If we make a big deal out of it, we might unintentionally teach our kids to feel left out or worry about missing out.
Best of luck with it all.