Salutations Dave,
Let’s test something, when you read or delete an email on your iPad, then sign in on Gmail’s webmail does that change reflect there? That’s going to tell us whether the issue is the push from your iPad to Gmail or Gmail to your iPhone.
Next, can you also test whether you’re able to send and receive email on your iPad? You can attempt to send an email from yourself, to yourself. That will test both.
If the changes on your iPad do not reflect via webmail, then what we’d like to have you do next is go to Settings > Mail > Accounts to remove and re-add your account on your iPad.
- Tap the email account that you want to remove.
- Tap Delete Account.
To add your account again, this article will walk you through it Add an email account to your iPhone, iPad, or iPod touch
How to set up your email account automatically
If you use an email provider like iCloud, Google, or Yahoo, Mail can automatically set up your email account with just your email address and password. Here's how:
1. Go to Settings > Mail, then tap Accounts
2. Tap Add Account, then select your email provider.
3. Enter your email address and password.
4. If you see Next, tap Next and wait for Mail to verify your account.
5. If you see Save, tap Save.
Thanks.