I was going to say exactly what NM suggested. Could this back-n-forth business be a result of his possible bi-polar?
If he has bi-polar, you have a hard road ahead and have to accept his new H. The one with serious depression. I know you have the strength to do this, but it's early days and this diagnosis is not really even confirmed, right?
What exactly did he say when he said he might have something "wrong with him"? Does he still have his cold? Is that what he meant, possibly?
The way I see your sitch is like this. WH wants to come back to you but he needs you to be moving forward, leading, and he, because of his problems, needs to be lead. This requires you moving on, moving forward, keeping your back to him. Don't face him head on, but every once in a while look back over your shoulder to check if he is following or not. But do not confront him and ask him "Are you following?". Because he will only be able to say "No" or "I'm not sure" or "I'm ambivalent". Be strong for your little girl, and for WH, who, we think, has some serious psychological issues which are gripping him. He's not reliable right now, but you are. He's weak now, you're strong. If you love him, love him by guiding him but asking him for nothing.
That's my take on it. But I totally get that you already have one child right now, and want a partner, not another child.