How would YOU manage the problem? You have two servers, server1 and server2, NOT server and server2, that you want data from.
What I would do is connect to server1, get the data, and do something with it. Then, I'd connect to server2, get the data, and do something with it.
But, your code has some real problems, aside from the poor names and blocking nature.
while (client.available() > 0) {
char c = client2.read();
Serial.print(c);
}
While client(1) has data, it doesn't make sense to read from client2.