why does kate tell chris she is worried about george's visit ? is this the real reason she is worried?

I don't see any evidence of Kate's worry when she's talking to Chris, but she does say the following to Joe.

"I don't know. (She speaks with warning) He's a lawyer now, Joe. George is a lawyer. All these years he never even sent a postcard to Steve. Since he got back from the war, not a postcard."

In this quote Kate alludes that George knows the truth and is coming after Joe. In this context, yes, she's very worried that people will learn the truth about her husband.