Couple of thoughts.
1) piCore doesn't have a network manager. If you are using both eth0 and wlan0, eth0 will be set as the default route. If you unplug eth0, the default route will not automatically change to wlan0. You have to manage that yourself.
2) What version of piCore are you running? The default 8192.ko driver in the 4.9.y kernels doesn't work well in piCore. (The same driver seem to work fine in full Raspbian).
One thing you can try..... this will try to use the nl80211 driver for wpa_supplicant first.
echo "nl80211,wext" | sudo tee -a /etc/sysconfig/wifi-wpadrv > /dev/null
echo "etc/sysconfig/wifi-wpadrv" >> /opt/.filetool.lst
filetool.sh -b
I have had nightmares with this driver it would work okay with some chipsets and not at all with others. In the end, I had to do the same thing that OSMC does, revert to an older realtek driver. To do this, you have to build your own kernels....which is a long story. (For the record 4.1.y kernels with the 8192 driver were only marginally better) So for right now, I would not recommend a wifi stick that uses the 8192 driver.