I have the following scenario:

I have a Cisco Aironet 1040 access point. I have it configured with two SSIDs, each going to a different VLAN. So:

SSID internal : VLAN 90
SSID guest    : VLAN 70

On the router side, I have a Cisco RV220W (with the radios now turned off) and have setup VLANs with like VLAN IDs.

VLAN 90    : 192.168.90.0/24
VLAN 70    : 192.168.70.0/24

As far as DHCP is concerned, each VLAN has a "DHCP Server" in the router's configuration:

So with the access point connected directly to the router, everything works great. I connect to the internal network, and I get a 192.168.90.x address, and the guest network gets a 70.xxx address.

Next I introduced a Cisco SG200-50 PoE switch between the router and the access point. The port is configured as a trunk port, so the VLAN tags should go right through the switch back to the router.

However, when something is connected to the access point, nothing works. It isn't able to get an IP address, and manually assigning one doesn't seem to let any traffic route.

Given that the access point works correctly when connected to the router directly, I believe the switch is misconfigured. What am I missing here? What can I use to better diagnose what the problem might be?

It's small business equipment, so CLI access is not available. Below are screenshots of the switch's config.

The access point is connected to GE2.