Provider A have transparent caching with squid .
In the situation which a client has multihome BGP with provider A and provider B then client does not send its outgoing traffic (upload) to provider A but its incoming traffic (download) comes to/from provider A .
In that situation what happens . clients will have problem to loading pages ? Cache works fine ? ....
If the connection comes through provider A, then it will simply be served by the cache. If the connection comes through provider B, it will go directly to the target server and fetch it from there.
The client is not aware that he gets served by a proxy.
All will be fine. The request reaching the server (client(1) in your post) comes from the transparent proxy ip not from the enduser (client(2)). So regardless which kind of routing is set, the server communicates with the proxy throught whatever link and the client comunicates with the proxy through provider A.