Maintain sticky across tiered VIPs

I don't believe this is achievable without performing at least SSL termination on both virtual server(VS) A and VS B. If you are performing SSL termination you can create 3 pools, one for VS A with WS1A and WS1B in them, then one with WS2A, and the final pool with only WS2B in it. You can then configure header insertion on VS A and have it insert a header with a value of WS1A for that server or WS1B for that server. On VS B you will have another iRule that searches for the respective HTTP header and then balances that traffic to WS2A if WS1A is found in the header or WS2B if WS2B is found in the header.

If these VS's are on the same F5s, and WS2A and B are using the same IPs as WS1A and WS1B you can do a match across virtual servers for persistence which should keep A to A and B to B.