Tabbed terminal that connects to a GNU Screen session

You cannot start a shell script from the screen session since it would inherit the old environment. You can however us a fifo to get the new environment variables into the old screen session. You can fill that fifo when you start your graphical session.

#!/bin/bash
FIFO=/tmp/your_variables
[ -e $FIFO ] && cat $FIFO > /dev/null || mkfifo $FIFO

# save number of variables that follow
NVARS=2
echo $NVARS > $FIFO
echo ENV1=sth1 > $FIFO
echo ENV2=sth2 > $FIFO

Start that script in the background on login (it will only terminate when all variables are read from it).

Now you can read from the fifo, e.g. add this function to your .bashrc

update_session() {
  FIFO=/tmp/your_variables

  NVAR=$(cat $FIFO)
  for i in $(seq $NVAR); do
    export $(cat $FIFO)
  done
  #delete the pipe, or it will not work next time 
  rm $FIFO
}

so that you can in your old screen session

update_session

You can run this: ssh -t hostname screen -r 3453 to reconnect. If you want to do it in a loop I use the following in a script.

while true; do
    ssh -t -o BatchMode=yes eeepc-rsi "screen -r 3453"
    sleep 2
done

This works best if you have ssh-keys setup so you can login without typing in your password. I'd also recommend that you look at tmux, a more modern implementation of screen. I actually use the above script with screen. You probably also want to use a named screen session rather than just using the pid like you do in your example.