I'd get a card and a small present (like a little easter egg or pencil set) for the child you don't know. I wouldn't take another present for the child you do know. This is because I hate turning up empty-handed at parties.
The other way is to take the mother you don't know a bottle of wine if the party is in a hall or at her house. Saves turning up without a present, and if the mums are running the party they will appreciate the wine. I might be alone in this idea though.
Presumably the other parents are clubbing together to hire a hall out in order to keep costs down (it's very unusual to hold joint parties like this btw: most parents want their child, and only their child, to be the star on the big day!)?
I wouldn't have thought that you would need to give the other child a present at all if you don't know them. Quite apart from the fact that, since they don't know you, they won't know who the present is from anyway! (presents are usually opened after the party is finished so they will be at home when they open the cards/presents)
You don't need to buy another present for the day of the party, if you have already given a present.
Parents normally send out thank you cards after the party, quite often stating that they loved the XXX that you got their child.
If you don't get one, just ask the mum "oh, did XXX like the present we gave?"
I did a joint party for my 2 youngest as their birthdays are within 2 weeks of each other and theyre only a year apart, but i was really surprised that some people bought a gift for them both. I thought it was sweet, but unnecessary