Thanks for getting back to us, Vaxadmin1.
Let's try to rule out all possibilities.
Are you using Wi-Fi or cellular? Does it occur with both types of internet connections?
Currently updated on iOS versions? Update your iPhone, iPad, or iPod touch - Apple Support
Be sure to restart both devices. Sometimes a restart can help resolve issues.
Are you using iCloud Messages? Use Messages in iCloud - Apple Support
If you're not using iCloud messages, do you have these settings turned on for the iPad? How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support
You did mentioned that all texts are blue, but the behavior sounds like someone is an SMS user: Send a group text message on your iPhone, iPad, or iPod touch - Apple Support
All responses in a group SMS are sent as individual text messages and the recipients can’t see the other responses from the group.
A good way to test to see if this is the case, do you have the option of leaving the group conversation? Leave a group text message on your iPhone, iPad, or iPod touch - Apple Support
To leave a group text, everyone needs to be using iMessage, which is an Apple feature. If you don't see the option to leave, it might mean that one or more of the users isn't using an Apple device with iMessage.
Have you tried deleting the conversation to see if that helps? You may want to backup any important messages before doing so.
Keep us updated.
Best regards.