Usually it's the other way around with wireless machines having problems joining a Homegroup.
Is there more than one router or access point in this network? Rebooting the router and making sure that everything is using the same default gateway, same subnet etc. might be a good idea but I'm sure you checked that, and the workgroup seems to be working as you mentioned.
You might try changing the Peer Networking services setting at ' services.msc from Manual to Automatic delayed start up which can sometimes fix this type of problem "first picture below" right click each service and choose properties to change the setting.
Another possible fix for this would be to first leave the current Homegroup from all machines in this network, then Delete all files
that reside in the PeerNetworking folder on each machine. This can often times fix join or leaving the Homegroup type of problems. After that reboot all machines then create a new Homegroup and see if anything changes.