It’s unfortunate that you hadn’t done your research. Processing for PR cards are taking multiple months and PRTDs can also take up to a few months depending on the office. Given that babies arrive very frequently anytime after 36 weeks traveling so close to your wife’s due date was always quite risky. If you have already sent in proof that your wife is due your only other option is to try and reach out to your MP who may be able to contact someone. I would include proof of your wife’s due date when contacting your MP and asking if they can help prioritize your PRTD processing as an emergency. Best of luck.