my suggestion you can try, just make the thing work with easy way
first you need to have linux pc with 2 network card
for the eth0 set ip for first network with thier gateway - > to the first network switch
for the eth1 set ip the second network w/o gateway -> to the second network switch
so from this pc you can go both line without any probolem
i hope this will help for temporary unless you happy with this way