I have been messing around with my yahoo email this morning. I set up my yahoo account to forward to my gmail account and works flawlessly. I get notification instantly without a hitch. With me forwarding my email to gmail it does not leave an achieve in my yahoo account which is nice. I have to learn more about the gmail account since this is all new to me.
One thing I did notice is if I send a test email from my X with gmail to my yahoo account it does not show up in my gmail inbox but if I click "all mail" in gmail it shows it. Not sure where it's hidden in gmail. Any ideas? If I send a test email from my X in gmail to my gmail address it shows up in the inbox and the same if I send an email from my yahoo to gmail.
Anytime you send an email a copy of it goes into your all mail folder. So it really didn't send it back to you.
I've tried this a couple of times using my Road Runner email account which is set up like yours. Gmail will check your other email accounts by how often you get email. If you get a lot it checks frequently, if you don't get much then it will check once or twice an hour. Usually when I send an email to myself at Road Runner I have to go into settings and have it check now. Then a couple of minutes later the email shows up.
I think you're getting the message. If you can and I know this might be difficult to do, try to switch over to Gmail completely. Start sending emails out with your Gmail address and maybe note that this is the address you want return mail sent to. IMHO Gmail is miles above any other free mail service.