No this isn't how a puppy should behave. A good trainer at the socialisation classes should be able to advise? To be honest, having two young puppies makes addressing this a greater challenge. he needs at least as much time alone as he does with your other puppy for example -- needs to work on his confidence, needs continued socialisation probably with some help from a good trainer (rewards based, NEVER 'corrections' based, using choke chains etc).
He will either be this timid due to genetics (ie this is unfortunately, his temperament) or due to his initial exposure (or lack of same) to the world by his breeder. Good breeders make sure puppies meet lots of other people, dogs, pups and so forth. If he was homed earlier than 8 weeks (ideally, older than that 9-16 weeks, the later the better) or was removed from his mother and siblings too young this also generally causes problems with socialisation that are challenging to address.
Because you have two puppies at the same time, you have a much greater challenge ahead -- especially with one very timid pup. For detailed reasons and guidance, read:
http://board.cavaliertalk.com/showthread.php?t=10549
and
http://board.cavaliertalk.com/showthread.php?t=30093
In general I'd recommend getting him back on his own, not with your other puppy, into a good, rewards based socialisation class and get some expert guidance so that you can work on this now while you have the best chance of tackling it. I'd look for a CPDT certified instructor. If this is a really ingrained behaviour, you will need to make adjustments to make the world comfortable for him -- but without hiding him away. That's why working with a professional is a good idea.
I'd also search 'shy dogs' or similar on the site as there are a few previous threads over the years with recommended books etc. For example
www.deesdogs.com has an excellent handbook for working with shy dogs. Anything recommended on
www.dogstardaily.com and
www.sitstay.com will also be an excellent choice.
Also with two pups so close in age, of opposite sex, be sure you spay/neuter at an appropriate age. This is more of a responsibility when they are so close in age and could mature unexpectedly leading to a litter. This will get very tricky in about two months. Your vet can advise on this issue and how best to manage it.