Presumably both laptops can access the Internet.

You may be encountering a wifi security feature provided in many wireless
products that prevents wireless clients from accessing each other directly.
I'd suggest looking through your wireless setup to look for things like
"wireless privacy" or similar features. So long as these are enabled, they
will not be able to talk whilst associated to that router's wireless.

If I try a traceroute, it doesn't even get out of the host computer to the
> router.


If both are on the same subnet, the router will not be involved. You should
be able to traceroute to external addresses through the router however.


> They can both ping the devices that are cable connected to my router. Yes,
> I don't know what I'm doing ;-)
>

That's actually an excellent test. Are the laptops and wired computers all
in the same subnet (e.g. 192.168.0.x)? If so, this make me suspect that
wireless security features are blocking your attempts even more.


> Is it possible to achieve what I want to do, or is it not possible to
> connect two computers this way if they're on the same wifi hub?
>

It is certainly possible, but the specifics may depend on your wireless
equipment.

Keep in mind, until the two laptops can "see" each other on the network,
using ping, ssh or whatever other tests you like, there's no sense fighting
with samba, sharing or any other service that depends on the underlying
networking.