...basically, I either don't believe "seductive" exists, or don't believe it's ever had a clear definition. The two are very similar.

It appears that you're trying to ask if "children" can ask others to engage in sexual activity with them... to which I have but one argument...

sat on the sofa, opened her legs and pointed down and said through gritted teeth "you want this?"

"Plain fact." There's no point in having long, drawn-out conversations about whether to engage in denial of observable reality, there's just... plain fact.

Speaking of which, I'm going to rip you a new one briefly...

I don't know why or whether she really understood what she was offering.

She understood quite clearly what she was offering. The question instead is whether you understood what she was offering.

See the difference? Her. You. Different people.

In this case...

Well she couldn't have gone far so I searched and then I reached the top of the stairs and found a trail of discarded clothing leading to my bedroom. In there I found a very naked little girl in bed with a very big smile on her face.

...I don't see that she was offering anything. She could have easily just commandeered your bed.

I've known children rather a bit younger than that who have... well, not so much "offered" as "very determinedly pursued" a number of ideas of theirs. This may or may not be one of them, but there's nothing explicitly there to suggest it is.

...and if so how should we react?

Hopefully, with more maturity than the child in your life. A lot of people fail that one.

Should we always be controlled...

Nah. We should never "be controlled," as this suggests a fascist dystopia with overseers.

are there times when it might be OK to have mutual physical love?

Mostly, it's physical pleasure. A good cuddle is physical love, a roll in the hay - as the metaphor goes - is physical pleasure.

'n of course it's okay. Frankly, it doesn't surprise me in the least that there are occasional atrocities in history when peoples' highest ethical debates are at best about crap with no ethical weight - you eat three meals a day, and this is the greatest ethical quandry you can come up with?!??!?

There is no ethical weight to mutually-desired pleasureable activity. There is great ethical weight in lying to conform to society - doesn't say yes, doesn't say no, does say not to be a raging jackass. There is even greater ethical weight against forbidding it.

~shrug~ Have fun. Your choices are between violent thugs, depending on jurisdiction, and doing something which is perfectly fine which you have been invited to do.

Your construction, meanwhile, sort of makes me wonder if you're a grad student somewhere. ;)

Have fun.