I would ring up the other mum (or dad ) and just explain the situation. Most other parents have no problem with you bringing younger siblings to events held in playcentres (when talking about this age group - ie, under school age), provided you pay for their entry. I have had to do it before, when DH has been away with army. If DH is here, I always prefer to try and leave the younger kids at home with him and let the invited child have their 'own' special time without the other siblings.

PS - the best thing about school age is you can dump the invited child and no-one has to stay with them!!