Script to connect with ssh to remote server with password

Given the requirements I would install expect on my local machine and use it to add in effect a new command. Let us call the remote hosts one and many1, many2 and the local machine mybox. Something like this (untested)

#!/usr/bin/expect
# connect to "one"
spawn ssh username@one
# next lines shouldn't be needed, should have shared keys for "one"
expect "assword: "
# provide password for "one", ending with "\r"
send -- "the_password_for_username@one\r"
# mainloop
interact "~p" {
    send "ssh manyuser@[lindex $argv 0]\r"
    expect "yes/no)? " { send "yes\r" exp_continue } "assword: "
    send "the_password_for_many\r"
    }

Run this on mybox as ./script many1, it will connect you to one

Then when you want to connect to many1 just type ~p. It will run the ssh command, answer the "do you want to connect" question if asked, and provide the password.

Of course the standard comments about the insecurity of storing passwords in scripts apply. The other slight downside is that you need to dedicate a key sequence to this. Here I am using ~p but you could use a function key.