yeah that does suck! Personally I escape ASAP but no-one should have to leave while they still don't feel ready to cope and need that extra support.
Can you ask for a transfer to the hospital after you give birth so that you get a longer stay?
Who are your support team in labour? I understand that you don't want to fight for a longer stay after giving birth so maybe your partner or any other support person you enlist could fight on your behalf.