Given that it would appear that it was only discovered that Amy's baby was part timelord after kidnapping her, how would they have known to do so to start with?

Time Travel perhaps.

I think it has to do with the legends of the Doctor. If you think about it the Doctor has never travelled alone. So they could have got it from that.

Not to get too technical, but what happened was:

wibbly-wobbly timey-wimey.

I'm paraphrasing, obviously.

The whole 'conceived in The Tardis therefore Timelord DNA' seems a little too contrived imo.

So maybe... The Silence had a poke about as there were questions how long she had been held prisoner in Day Of The Moon, as I seem to recall. Maybe that scene has something to do with it all.

Maybe.

Probably not as she would have been a ganger then.

I get the feeling that in a completely different timeline, one where Melody does not get kidnapped, she grows up on board the TARDIS as a female Timelord.

Therefore the purpose of kidnapping Amy whilst pregnant is to capture Melody from birth and turn her against the Doctor as a weapon - thus changing established history (in a future timeline).

Kinda like what the Terminators were trying to do by going back in time and killing John Connor.

Which is why I think we are getting the Hitler episode next - to spell out to us in advance the repercussions of changing established events in a timeline.

River could well be a fixed point in history.

Which could also mean that the River we know and love is NOT the same version of the Melody Pond who has been kidnapped. Our River could be the original timeline version sent across to this universe to try and correct the time stream.