Your setup is a little strange. The idea of the router being on it's own VLAN doesn't make a lot of sense.
Typically one would setup a 'management' VLAN that encompasses all switches and routers. This of course would be used to manage all the hardware. This VLAN would be "tag all" and carry all VLAN's between switches and routers.
Then you would segment your network with separate VLAN's depending on needs. Your DHCP server(s) and DHCP relay agents should be on the same VLAN(s) as the client's that need to access them. Having DHCP on a separate VLAN just add's complexity and more room for problems.
Let's say you have 3 departments you need to keep segmented for security reasons. You would have the following:
VLAN 1 = management VLAN = 192.168.1.0/24
VLAN 2 = dept A = 192.168.2.0/24
VLAN 3 = dept B = 192.168.3.0/24
VLAN 4 = dept C = 192.168.4.0/24
Subnet Mask for all = 255.255.255.0
You would setup all VLAN's and the appropriate IP address scheme on the Core switch and configure your routing. All VLAN's should route through the management VLAN. Your core switch would have 192.168.1.250 as it's IP address. That would also be your main internal DG for the management VLAN. All switches in your network would have IP's in this range.
So let's say you have 3 switches, one per dept.
Switch 1 IP = 192.168.1.249
Switch 2 IP = 192.168.1.248
Switch 3 IP = 192.168.1.247
All 3 switches would have 192.168.1.250 as their DG address (the core switch).
If your core switch is layer 3, I would use it for internal routing (easy since in this example, you're not sharing between subnets) and have it point to the router for external access. Your router of course would have to have an IP in the same management VLAN's range on it's internal interface. The external interface would of course be the IP provided by your ISP.
This is of course a very basic design. Because of the VLAN tagging, you could have all 3 VLAN's running on all 3 switches if you want and they wouldn't be able to communicate with each other giving you your segmentation. If you did need two of them to communicate, you set that up in the core switch or router.
If all 3 VLAN's require DHCP, you would put a DHCP server in each VLAN and relay agents if necessary. This also segments the DHCP so there's no chance of the wrong client picking up an IP in a different VLAN. Clients can ONLY contact the DHCP server in their VLAN(subnet).
Your setup is a single subnet from what I see in your post so I wouldn't even bother with VLAN's in this case. Just put everything in the same subnet.
