For this to work, I recommend moving all L3 information from the Ethernet interface on the router and placing that information on the core switches, let them perform intervlan routing.
Router on a stick is useful when you don't have L3 switches but from your post, it seems you do.
I don't think the router would allow you to create another LAN interface using IP addresses on the same subnet as the current one.
For instance;
f0/0.1
en do 1
ip add 192.168.1.1 255.255.255.0
int f0/1.1
en do 1
ip add 192.168.1.2 255.255.255.0 (this will fail)
On the core switches, you can do this with SVIs.
On Core 1
int vlan 1
ip add 192.168.1.1 255.255.255.0
On Core 2
int vlan 1
ip add 192.168.1.2 255.255.255.0
You can even go as far as creating HSRP between the two by inserting the following commands under each SVI.
standby ip 192.168.1.3
standby priority 110 (Core1)
standby preempt (Core1)
