I'm certainly no expert on these things, but you have witnesses, so proof shouldn't be a problem. Depending on what the expenses are and what the limit is in small claims court in your area, you could take them to small claims court. Again, that all hinges on if the limit is enough to cover all costs.
I am sooooooo sorry this happened. I can not even begin to imagine how terrifying that must have been for you and your babies.
for Merlot. I hope he makes a full recovery.
Another thought, have you contacted the owners of the pittbull and just asked them if they'd be willing to pay? There's a chance that they would do the right thing...I would hope.