You are going to have to setup dot1q trunking between the switches and the router (BTW did you mean 3825?) and then create a vlan interface on the router. You will not be able to have two router interfaces within the same IP address subnet otherwise.
You may need a switching module in the router for this to function as desired -- such as the NME-16ES-1G.
[edit / additional information]
You will not be able to have two router interfaces in the same subnet unless you either: (a) use a BVI interface as Vatine suggested (there are performance and other considerations using them however) or (b) put the two physical interfaces into a vlan (see example below).
!
interface FastEthernet0/3/0
switchport access vlan 10
switchport mode access
!
interface FastEthernet0/3/1
switchport access vlan 10
switchport mode access
!
interface FastEthernet0/3/2
switchport mode access
shutdown
!
interface FastEthernet0/3/3
switchport mode access
shutdown
!
interface Vlan10
description Server_Vlan
ip address 192.168.10.1 255.255.255.0
!
If you have two routers, then you could provide IP address/gateway redundancy for the servers by using HSRP, VRRP or GLBP.
[edit / additional information (HSRP example)]
interface Vlan10
description Server_Vlan
ip address 192.168.10.2 255.255.255.0
standby ip 192.168.10.1
standby priority 150
standby preempt
!
For your second router, change Vlan10 to ip address 192.168.10.3 and a priority of 140. Use the command "show standby brief" on both routers to confirm HSRP operation.
Best Answer
From what it sounds like you want the gateway to be redundant and also provide load balancing. The Cisco way to do this would be to use Gateway Load Balancing. If you just want the redundancy, HSRP and VRRP can do this. All of these happen on the router itself.
As far as having redundant connections to the switch from the servers you can do that with various forms of NIC teaming/bonding.
I still don't fully understand all of what you are asking, but maybe the above helps. One thing I can say for sure though is "not having access to the router admin" is just dysfunctional, and I don't think you are going to have a good solution that doesn't involve the router.