Your problem here is that you said "no siblings" and now you are backing out of that. That's going to irritate the other families who already arranged for sitters. I don't understand why this friend doesn't drop her child off at the party and take the 3 year old with her. Am I missing something?
If the point of "no siblings" is not to pay, that's one thing. If the point is to keep the party manageable and just for 5 year olds, that makes sense. Frankly, you shouldn't have to say that - if you invite little Susie to join your Janie at her birthday, why would Susie's family assume that 3 year old Patty can just come along? I don't get that and never did. Perhaps the tradition in your social circle is that entire families come, parents stay and need to be fed, etc. But then again, you said "drop off optional" so you assumed that many would stay. Maybe 5 years old is just too young for a venue party at a noisy place or the parents aren't sure there is enough supervision.
I guess you're in the situation now, so your best bet is to pay for the 3 year old and just hope the other parents aren't annoyed at you. I think it would be awkward to collect $10 from this mom at this point. If you are having a huge number of invited kids and this is likely to mushroom, then that may be another story and you will have to allow each family to pay, and just deal with the crowd.
Good luck - sounds like a tough situation!