I do not find any contradiction between John Donne's Holy Sonnet 14 and his Satire 3. In Satire 3, John Donne is telling people how important it is to see to their faith, while Sonnet 14 speaks about his personal struggle to do so.
In Satire 3, there is "anguish and anger" in Donne's tone as he speaks of "fair Religion." His tone throughout gives examples of how one must live to avoid losing all to "the enemy." There are three "key" themes in Satire 3:
A warning to those who fail to see the importance of spiritual truth
The challenge to ‘seek true religion’
The need to follow one’s conscience at all costs or risk damnation
Donne explains how terrible it would be for one's dead father to meet "blind philosophers" in heaven and later hear that his son was damned to hell. He implores his listener to fear damnation: that it is brave to do so:
Oh, if thou dar'st, fear this;
This fear great courage and high valour is.
Donne identifies the devil as man's foe. He implores the reader to stand fast to what is required of him, to protect the world God has created, as he has created us. Don't act bravely: be brave!
Courage of straw!
O desperate coward, wilt thou seem bold, and
To thy foes and his, who made thee to stand
Sentinel in his world's garrison, thus yield,
And for forbidden wars leave th' appointed field?
Donne explains that to ask a question of righteousness is not wrong. He tells the reader not to follow the dictates of a king blindly. He tells us to seek truth...
...though truth and falsehood be
Near twins, yet truth a little elder is;
Be busy to seek her...
Satire 3 puts forth the need for us to live spiritual, God-filled lives, and ways to do so.
Holy Sonnet 14 notes the imperfection of mankind and the poet's struggle to live the spiritual life he implores all men to live. Donne begins his sonnet speaking of how he wants the Father, Son and Holy Ghost to change him:
Batter my heart, three-person'd God...
He alludes to scripture text that presents the person of Jesus waiting for entrance into one's heart, found in Revelation 3:20 (NIV):
Here I am! I stand at the door and knock. If anyone hears my voice and opens the door, I will come in and eat with him, and he with me.
Donne relates to that verse when he writes:
As yet but knock...
Knocking infers a request to be admitted. Donne is saying, don't just knock—do more; and he uses strong verbs in asking the Lord to change him. Donne asks first for a new life:
...breathe, shine and seek to mend / That I may rise...
This may allude to the forgiveness of his sins ("mend") and his resurrection ("may rise"). When the author "stands," he asks God to...
...o'erthrow me, and bend
Your force, to break, blow, burn, and make me new.
The author knows that his mind ("Reason") is taken over by sin and proves him "weak or untrue." He admits that he loves God "dearly," "But am betroth'd unto your enemy..." referring to the devil. Aware of his sinful nature which he fights but can never defeat, he asks God to make a break with him ("Divorce me"), but then to bring him back into God's presence:
Take me to you, imprison me...
Donne believes that unless God captures him, he will never be free: this is a paradox—that only being taken by God will he be free.
Satire 3 relates that a man must seek out God, and then live a spiritual life. Holy Sonnet 14 speaks of how hard it is to do so—that man cannot succeed without the power of God sustaining him in the face of sin.