the easiest way to achieve this is to configure 3560 in location A with the lowest bridge priority for all VLANs to ensure that it's always the root bridge in your spanning-tree domain. Make sure that your triangle is symmetrical, meaning that you have the same number of hops and interface speeds on both paths:
3560 - BRIDGE-A1 - BRIDGE-B1 - LINKSYS - BRIDGE-B2
3560 - BRIDGE-A2 - BRIDGE-C1 - LINKSYS - BRIDGE-C2
this will ensure that BRIDGE-B2 - BRIDGE-C2 link is in spanning-tree blocking state, and will come up only if some other link fails
if your triangle is not symmetrical and/or if you have a different setup, then you might also need to modify spanning-tree port costs on some of the links. For example, you need to make your B-C bridge link with a large path cost (on each vlan)