I've already said so in the (much) older thread touching the same subject, but I think he keeps her around out of
curiosity and honor-bound gratitude. So, he lets her follow him around. And since Sesshoumaru rarely seems to be in a
rush to get somewhere, she doesn't really have much problems keeping up. (The riding animal helps too, of
course.)
The only two times I've seen Sesshoumaru use the Tenseiga has also been out of curiosity and/or the fact that the sword
itself has urged him to use it. The first time was more of a test run, and. again, that he probably felt compelled to,
since she made a conscious effort at getting him back on his feet.
All this is mostly guesswork, though, seeing as Sesshoumaru doesn't seem keen on getting close with anyone. Sadly, the
only part I saw him actually working with anyone has been anime filler episodes, so his... well, original... stance on
life and everything is still up in the air.