Don’t confuse your sentence tags with your dialogue tags (‘he said’, ‘she said’, etc). Though they might sound like the same thing, they are actually quite different.
A sentence tag or question tag is where a sentence begins as a statement but then the final element of that sentence concludes in a question. For example:
‘It’s really cold outside, isn’t it?’
‘Caitlan was supposed to be coming to this game, right?’
As you can see, the sections after the comma change the sentence from a statement to a question. But just because the last section of the sentence is a question, does that mean the entire sentence must now end in a question mark? Yes. When using a sentence tag, a question mark is required.
But what if the sentence tag is not at the precise end of the sentence? I would argue that, in the following examples, a question mark is still required.
‘It’s really cold outside, isn’t it, what with all the wind and snow?’
‘Caitlan was supposed to be coming to this game, right, even though she was sick?’
Though sentences like this do seem a little clunky, they are present all the time in spoken English. It’s probably got something to do with the fact that humans want to engage other fellow humans in conversation—by offering them a chance to voice their opinion—rather than just state a fact and move on.
I would recommend using sentence tags in the middle of a sentence as sparingly as possible and, instead, reword them for more formal writing projects.
Of course, characters can talk however they like! Who are you to stop them, after all?