execute normal command doesn't work

let g:temp=eval('"'. g:temp .'"')

after

let g:temp=escape(matchstr(g:str,'\(\t\)\@<=.*$'),'<')

Extracting this into a :function:

function! Literalize(string)
    " get already properly escaped sequences out of the way, so we don't double-escape them
    let s = eval('"'. a:string .'"')
    " escape remaining special key sequences
    let s = escape(s, '<')
    let s = eval('"'.   s      .'"')
    return s
endfunction

Explanation

The problem was that escape() handles its input° and output strings as a literal-string (as in single quotes ''). So escaping the < in "<C-w>" results in '\<C-w>', not the desired "\<C-w>"/'^W'.

° If the input is given as a double quoted "string", its escape sequences are evaluated by the vimscript parser, before it is passed to escape().

In your first line, the <C-w> is not escaped, so it appears to be matched as a literal string, and the escape function doesn't convert it to the ^W character.

So to get what you want, the first line should actually read

let g:str="move to right win\t\<C-w>h"

In addition, according to the documentation here at sourceforge, the escape command doesn't work how you appear to think. It's going to escape just the '<' character, which does nothing.