To be honest with you I wouldnt be attempting third position at all yet, unless of course you are learning it before first position. Hitting the correct note is a matter of a few things one of which is muscle memory. 

I myself used suzuki intonation to start ear training, along with scales in first position, then after becoming confident in first position started to learn to shift to third. if your teacher is as good as you say and I have no doubt he or she is they should teach you how to shift, and what the scales sound like till you have them memorised.

One way to shift on the a string to d, is play the b, with first finger, then c with second finger, then d with third finger, after you play the d, slide your entire hand up the neck until your first finger is on the d you just played with your third, yoqu are now in third position, after you practice this for a long time you will get a feel for were your finger goes. everyone struggles with intonation, even pros practice it all the time, one of the differences with a pro is that if they hit the wrong note they can correct it so fast you cant hear it.

Others on here will be able to advise you better than me and may have other ideas.