Hi,
I recently did this from LGW to MCO - you will need to all turn up at the check-in desks together. They are pretty strict on the check-in times and we had to wait until 4pm literally before they'd take our bags.
I didn't try the SSCI, but would suspect you'll need to go to a desk as you have an under 12 with you.
In addition anything you do check-in is not accessible until you reach the other end, you can't check the bags in and then bring them back in the morning, you need to hand them over at that time. I am sure you could check in additional bags the following morning, but if you're there and it's practical depending upon your circumstances try and do them all at the same time.
Hope this helps.