I have a single AP1252 unit with two SSID's (Private=VLAN1 & Public=VLAN3). The SSID:Private is the native VLAN and works just fine. The SSID:Public has client problems. From the AP, I can ping my VLAN3 gateway on the router. Clients can connect to SSID:Public and in the GUI, it shows the association. But the client can't get an DHCP address from SSID Public. I set a static IP address on the client on VLAN 3, but still can't ping the gateway. I'm not sure where I went wrong.
Your configuration looks perfectly fine. Something is not right on your switch/router/dhcp side.
SWITCH, make sure you are trunking:
switchport trunk encapsulation dot1q
switchport trunk allowed vlan 1,3
switchport mode trunk
spanning-tree portfast trunk
On router, make sure you got helper pointing to DHCP, or you have a DHCP pool configured for vlan 3.