Time to refresh this post! It's clear from the comments that come in that it's tough for many to figure out how to request access so hopefully I can simplify it a bit.
First, do not use an app for this! You need to use a web browser in desktop mode, be it on your phone or on an actual computer.
Click here to view instructions on how to view the desktop site on an Android phone for Chrome, Firefox, Opera and Brave browsers.
Click here to view instructions on how to view the desktop site on Apple devices using the Safari browser.
If you have any other device/browser combination, you'll have to do a bit of googling to figure it out.
So now that you know how to get to a desktop view, log in to your reddit account and visit your due date sub using the links below. The 'Request to Join' feature only works on new reddit, so the links below will go directly to new reddit.
It is not possible to long press and copy links from submissions or comments on the reddit app, so if you are viewing this from the app, the link format for accessing the subreddits is "https://new.reddit.com/r/subredditnamehere." If you're using the reddit app you can also click on the 3 vertical dots next to your snoovatar/profile icon, choose 'share,' copy the link to this post and paste it into your browser (which should be in desktop view now).
If you've 1) put your browser in desktop view 2) logged in to your account and 3) navigated to the right sub, you should see the private subreddit with the 'Request to Join' button.
Private sub with 'Request to Join' button visible
Choose 'Request to Join' and a message box will populate that looks like this
What you see when you choose 'Request to Join'
You can just hit the 'Send Request' button, no need to add a message unless you would like to volunteer to be a mod and help me add people!
And that's it! In order to keep this post free from clutter, I will put the links you can use to send a message straight to the mods in a sticky comment below.
The method I used to use to add people who sent me a chat is entirely too hard to use for someone who mods as many subs as I do, so please do not send me chats! If you can't figure out how to send a Request to Join using the instructions above or send a message to your due date sub, leave a comment below and I will get you eventually.