This is how POP accounts work. I'm not sure how the Yahoo account works on the iPad is set up. Sometimes it acts like IMAP, and sometimes POP. However Yahoo only offers POP accounts for desktop clients.
Here is the difference. POP accounts simply download email from the server. They can be set up to leave it there, or delete it on download. You can also tell it to delete the email when it is deleted on the client. What will not happen is for the server to tell the client to delete an email.
IMAP accounts do everything on the sever. If you delete an email on one client, it is immediately removed from the server. Because the other clients are always kept in sync with the server they update immediately also (or as soon as they connect again).
So here are the two things that might be happening. You Desktop automatically downloads the email throughout the day. Yahoo acting as an IMAP account faithfully deletes each email from the server, but because the emails are already on the desktop, they stay there. POP has no way to tell the desktop to delete mail.
Or, Yahoo acts as a POP account set up to leave mail on the server which for a secondary and mobile client is usually the safest bet. After all, if you delete an email permanently on a mobile device using POP, that mobile device contains the only copy, in Trash. Not the most convenient place to try and recover stuff from.
Then the desktop accesses the server when you get home, and downloads the emails again, because the device, prudently, left them there.
Either way there isn't a lot you can do about it. There are no settings on the iPad you can make to change it's behavior.
If the second scenario is what is happening though, you can chose to go to your Yahoo Mail in Safari on the iPad. Since your actions there delete email directly on the server the desktop can not download it later.
If the first scenario is true, close your email client on the desktop before leaving home so that it can not update while you are gone.
Or, go to your email on both the desktop and iPad using a browser. That way you are changing everything in the same place, on the server. You may have to revert back to the Mail app when dealing with some attachments.
