can someone see my text messages through another source and not my phone

What exactly do you mean through another source?

Cause the only way I can think to answer this question is by stateing -

If you send them a text message on another device or to their email, yes. otherwise no well unless you like emailed those to yourself and "someone" has access to your email etc etc etc yes...

NO, my husband claims he sees all my texts In his phone. Is this possible?

If he is signed into Messages with the same Apple ID, then yes.

GB

can he see any and All my texting or when I use iMessage texting?

how come I can't see his or my kids texting which we all use the same Apple ID?

how can I fix this issue?

You would need to get a separate Apple ID. Devices signed into the same Apple ID running iOS 8 or higher share services signed in to that Apple ID like Messages, Mail, FaceTime, etc.

Cheers,

GB