I am no expert in networking, but i think you should be able to if you set it up right.
The router right after the internet source ( router1) should be set to 192.168.0.2 and leave router2(192.168.0.103) as it is. From 'My computer' pc see if you can ping the printer ( 192.168.1.100).
If you can , then 'My computer' pc shouldn't have a trouble in adding a network printer. You do it by going to control panel>>printers>> add a new printer>> Network printer>> you can either browse for it or in the second field type in \\192.168.1.100
The key is to have all the devices on the same subnet and preferably same IP class.
If the above fails, you can try configuring the printer to be in the 192.168.0.2xx range by setting DHCP server in router2(192.168.103) to the above range. Or better yet, let router1 handle all the ip assigning and make it the main DHCP server and disable DHCP in router2. So that way, all your devices should have ip's in the in 192.168.0.10x range.
Your last solution would be looking into web-based printing. Some info about it
here