He wasn't happy to send her away, but he did it. And he was most absolutely unhappy -- I might even go so far as to say "angry" -- when she returned and refused to leave his side. Just for a moment, but it was tense enough that I was worried they'd end up parting on bad terms.

Well, yes, of course he was pissed off. He sent her off so that she'd be safe and she went right into the lion's mouth again. I also notice that he brought up two anti-gravity grips, so I'm sure some part of him was aware that she'd come back to him (as she did in The Parting of the Ways).

It reminds me, actually, of a quote from another show -- "She was curious. That's why Fred didn't put it into containment immediately. How things work. What makes them special. She was always searching for what other people couldn't see. She was just curious. I think I hate her a little for that."

She wanted to know more about an object and it ended up killing her and he hated that, despite adoring her with every fiber of his being.

The Doctor loves Rose's independent streak and her loyalty and love for him, but hates it when those things puts her in danger. It's nothing that I haven't seen in dozens of other love stories. It's quite common, actually.