What are normal reactions to have to his stbx?

[Gecko]

He wants us to move in together. Says it will solve the issue, as I nearly left the relationship a week ago because of the 'closeness'...

Huh??? Is this guy an idiot? You're moving in isn't going to solve anything...in fact, it would make things worse! Sure, the SBTX might not come over as much if you are there and so he won't be put in the position of having to defend her, but what is going to happen is that she is going to say thing to him like "we got along fine until SHE (meaning you) moved in" and then he'll come up with some kind of [lame] excuse (blaming you) and before you know it, he'll actually come to believe the problems between him and his STBX and between him and you ARE your fault because you're "jealous" and controling.

Last round of questions to you helpful folks - I've met her a few times and we've been civil, no more, no less. If I were to agree to move in, I'm inclined to have a sit down with either her or the both of them and settle this issue, as well as to make sure that I'm accepted as a 'stepmom', and to let her know that I respect her position as the mother of child, but not as the everpresent ex.

What you might view as a well-meaning and logical course of action, she will most likely view as an attempt to control (been there, done that).

My advise to you is this: RUN FOREST RUN!