I think that this can be answered in two parts.
1) Does the Quran say that Christians believe in the divinity of Mary mother of Jesus.
Yes, it sort of does. Though it does not necessarily imply that all Christians believe that, nor is it explicitly stated that the established concept of Trinity is the divinity of God, Jesus and Mary(rather than the Holy Spirit). Indeed the Prophet Muhammad(p.b.u.h) interacted with diverse sects that were present in his region at his time and they had diverse beliefs.
Its true that most mainstream Christian denominations today and even in the past did not consider Mary to be divine ... but fringe sects have existed that believed that, see Collyridianism for an example. Some of these sects were present in the time of the Prophet Muhammad(p.b.u.h) and interacted with him and so God revealed verses of the Quran regarding their beliefs. Furthermore, in the strict Sunni view at-least, Catholic reverence for and prayer to Mary would fall under the definition of shirk.
2) Does the Quran misinterpret the canon Christian belief of Trinity? Specifically does it mix the Holy Spirit with Mary, mother of Jesus?
The Quran mentions the word three as applied to Christian belief in two different places 4:171 and 5:73. Its not explicitly stated what this belief is but in the first instance the Quran goes on to reject the divinity of Jesus and the angels(4:172) ... keep in mind that the Holy Spirit is the Angel Gabriel in Islamic belief.
4:171 O People of the Scripture, do not commit excess in your religion or say about Allah except the truth. The Messiah, Jesus, the
son of Mary, was but a messenger of Allah and His word which He
directed to Mary and a soul [created at a command] from Him. So
believe in Allah and His messengers. And do not say, "Three";
desist - it is better for you. Indeed, Allah is but one God. Exalted
is He above having a son. To Him belongs whatever is in the heavens
and whatever is on the earth. And sufficient is Allah as Disposer of
affairs.
4:172 Never would the Messiah disdain to be a servant of Allah, nor would the angels near [to Him]. And whoever disdains
His worship and is arrogant - He will gather them to Himself all
together.
Again, Angel Gabriel is the Holy Spirit in Islam:
16:102 Say, [O Muhammad], "The Pure Spirit(Ruh al Qudus cognate to Hebrew for Holy Spirit ) has brought it down from your Lord in truth to make firm those who believe and as guidance
and good tidings to the Muslims."
2:97 Say, "Whoever is an enemy to Gabriel - it is [none but] he who has brought the Qur'an down upon your heart, [O Muhammad], by
permission of Allah, confirming that which was before it and as
guidance and good tidings for the believers."
2:98 Whoever is an enemy to Allah and His angels and His messengers and
Gabriel and Michael - then indeed, Allah is an enemy to the
disbelievers.
In the second instance, the Quran goes on to establish the Humanity of Jesus and his mother Mary.
5:73 They have certainly disbelieved who say, "Allah is the third of three." And there is no god except one God. And if they do not
desist from what they are saying, there will surely afflict the
disbelievers among them a painful punishment.
~
5:75 The Messiah, son of Mary, was not but a messenger; [other] messengers have passed on before him. And his mother was a supporter
of truth. They both used to eat food. Look how We make clear to them
the signs; then look how they are deluded.
Ibn Kathir, discusses this in some length while commenting on 5:73. Unfortunately the abridged version available in English is incomplete. You can see the full arabic version here, see last paragraph of page 1 and first para of page 2. I'll try to give a rough translation. Ibn Kathir mentions two opinions, he mentions
Mujahid who said that the Christians believe in a Father, a Son and
the Word who issued from the Father to the Son. They differed about
the three and had various sects with diverse beliefs, each of which
declared the other a disbeliever, while in truth they were all
disbelievers.
Ibn Kathir also mentions the opinion of Saddi:
who said that they believed that Jesus and Mary are Allah as detailed
later on about God's dialouge with Jesus on the Day of resurrection. I believe this is the more correct opinion, and God knows best.
The point is that its not Islam's job to define Christian beliefs and terminology as they evolved and diverged through time and geography. Islam rejects the divinity of any person or being other than Allah, it rejects the divinity of Angels, the Holy Spirit and Mary ... and it rejects the belief that Allah and Jesus are the same person (5:17).
