Login by ssh , exec one command and i don't want to quit the bash

sudo -i runs a login shell as the target user. The rest export PS1... would only be executed after that shell has terminated.

Also, your ~/.bashrc is likely to override PS1 to passing it in the environment will probably not help.

You could try:

ssh -t host 'sudo env PROMPT_COMMAND="PS1=\"Remote! \W: \"
             unset PROMPT_COMMAND" bash -l'

(assuming the target user's ~/.bashrc doesn't set $PROMPT_COMMAND).

This appears to work:

ssh -t localhost "echo '. /dev/fd/2'|sudo bash -sil 2<<\FILE        
PS1='my prompt : '
exec 2>/dev/tty
exec </dev/tty
FILE
"
[sudo] password for mikeserv: 
my prompt : id
uid=0(root) gid=0(root) groups=0(root),1(bin),2(daemon),3(sys),4(adm),6(disk),10(wheel),19(log)
my prompt : 

sudo will close all file descriptors but 0,1,2 by default and it wants <&0 on a terminal for the password, but you can often sneak by with hijacking stderr. And it's not gone for good, anyway - practically the first thing I do above is reconnect it to ssh's terminal. More realistically you'd have some actual script that you would pass through like $(cat file) where my $PS1 definition is and the rest. It's a lot of annoying indirection, though; it would be better I think to instead handle that stuff as neccessary in remote profiles.