If I bring up a concern or my feelings about situations my husband often tells me we shouldn’t talk about it and I should respect that. Then he said he would do something specifically to make amends for a transgression and then dropped the ball. When I mentioned it he said I needed to let it go. So therefore with all of this, he said he can not pray with me since Matthew 5:23-24 states “Therefore, if you are offering your gift at the altar and there remember that your brother or sister has something against you, leave your gift there in front of the altar. First, go and be reconciled to them; then come and offer your gift. I am just at a loss. Any feedback would be greatly appreciated.
It sounds, having only one side of the story, that your husband has a hard time admitting to having done wrong. It sounds, too - again having only your side of things to go by - that he doesn't know how to talk things out with you constructively. This won't change simply by trying to force him into conversations he knows he is not properly equipped to have with you and so is avoiding. He needs, together with you, to learn how to work through conflict with you. It seems you will have to show him how to do so, or, alternatively, go together to a Christian relationship counsellor who can guide you both into a better, biblical engagement with each other over points of conflict.
If your husband committed to making amends and he hasn't and doesn't intend to, he has compounded his wrongdoing. Nagging him about his broken promise, though, will not produce a good result. Instead, go to God in prayer and ask Him to be relentless in his conviction of your husband. Not simply to satisfy your sense of justice, not so you can get your "pound of flesh" out of him, but so that your husband's relationship with God won't be hindered. This is God's chief concern in regards to your husband, even if it may not be yours.
In all things - including your marriage - God intends to make you both increasingly like Jesus.
Romans 8:29
29 For those whom He foreknew, He also predestined to become conformed to the image of His Son, so that He would be the firstborn among many brethren;
2 Corinthians 2:14
14 But thanks be to God, who in Christ always leads us in triumphal procession, and through us spreads the fragrance of the knowledge of him everywhere.
2 Corinthians 4:7-11
7 But we have this treasure in jars of clay, to show that the surpassing power belongs to God and not to us.
8 We are afflicted in every way, but not crushed; perplexed, but not driven to despair;
9 persecuted, but not forsaken; struck down, but not destroyed;
10 always carrying in the body the death of Jesus, so that the life of Jesus may also be manifested in our bodies.
11 For we who live are always being given over to death for Jesus’ sake, so that the life of Jesus also may be manifested in our mortal flesh.
Above all else, this is God's priority for both of you in your marriage. Is it yours? Is this your priority in your dealings with your spouse? Or do you just want your husband to admit his wrongdoing and do what you want him to do to make you feel better about it?
Matthew 5:21-26
21 “You have heard that it was said to those of old, ‘You shall not murder; and whoever murders will be liable to judgment.’
22 But I say to you that everyone who is angry with his brother will be liable to judgment; whoever insults his brother will be liable to the council; and whoever says, ‘You fool!’ will be liable to the hell of fire.
23 So if you are offering your gift at the altar and there remember that your brother has something against you,
24 leave your gift there before the altar and go. First be reconciled to your brother, and then come and offer your gift.
25 Come to terms quickly with your accuser while you are going with him to court, lest your accuser hand you over to the judge, and the judge to the guard, and you be put in prison.
26 Truly, I say to you, you will never get out until you have paid the last penny.
Why your husband concludes from this passage that he can't pray with you I don't know. But he is certainly, from what you've indicated, the very sort of man spoken of in this passage who has a brother (or, in your case, a sister) with something against him who needs to "come to terms quickly" with his sister lest the Judge (who is God) throw him into prison. I don't see, however, how this passage prevents him from praying with you...
In any case, you
both, in the situation you've described, have commands of to follow. On your side of things, God tells you:
Matthew 18:32-35
32 "Then summoning him, his lord *said to him, 'You wicked slave, I forgave you all that debt because you pleaded with me.
33 'Should you not also have had mercy on your fellow slave, in the same way that I had mercy on you?'
34 "And his lord, moved with anger, handed him over to the torturers until he should repay all that was owed him.
35 "My heavenly Father will also do the same to you, if each of you does not forgive his brother from your heart."
And,
Ephesians 4:31-32
31 Let all bitterness and wrath and anger and clamor and slander be put away from you, along with all malice.
32 Be kind to one another, tenderhearted, forgiving one another, as God in Christ forgave you.
If your husband wants to play games with you spiritually, refusing to pray with you so long as you hold him to his promise to make amends, then you'll just have to pray alone. Prayer, after all, is between you and God. If all is right between you and Him, He will hear you whether or not your husband is praying along with you.