Your desire to pray more and to have peace in your heart is itself precious to God. He looks at the heart and He values what is in the heart to do. Like David who had it in his heart to build a house for the Lord, God credited him for that desire even though he was not the one to build it. When you bring this honest longing to Him, He already sees it and counts it as good.
The peace you are asking for comes in a certain order. Scripture always says grace and peace, never peace and grace. You will not find real peace in your heart by trying harder to feel peaceful. Peace comes as you come to know more deeply the grace of God toward you through Jesus Christ. God has made a way to have peace with you through the work of Jesus, where mercy and righteousness meet. When He speaks to His people, His word is peace.
It may help to know that prayer is not measured by length or by perfect concentration. The prayers recorded in the Bible are often very short. God hears a sincere cry like, God be merciful to me, a sinner. What matters is not that you pray for an hour without a wandering thought, but that you pray from your heart and truly mean what you say to God. Distraction does not disqualify your prayer. God knows your frame and He still invites you to come.
Prayer is also much wider than only asking for things when you are in trouble. It is sharing your heart with God, telling Him your feelings, worshiping Him and being aware of His greatness and glory. Its main purpose is not to get your wishes done on earth, but to open the door for His will to be done in you and through you. When your heart wants His will, He is free to do what He has long wanted to do for you without forcing your will.
That is why the best prayer for distraction and restlessness is to ask God to work in your heart. One psalm prays, teach me Your way, Lord, and unite my heart to fear Your name. Another says, blessed are the pure in heart, for they shall see God. Ask Him to create in you a clean heart and to give you an undivided heart that wants Him above all else. He is the one who can cut away what divides your heart and make it whole toward Him, and He responds to a willing heart that comes to Him because it wants to, not because it is forced.
You can come to Him simply and honestly throughout the day. A short, heartfelt prayer in the moment you feel distracted is more pleasing to Him than long words you do not mean. Bring your love, your thanks, and your needs together, and ask Him to align your heart with His purposes. As you keep turning your heart toward Him in this way, and as you take responsible steps to set aside quiet moments to seek Him, He will grow in you both a stronger habit of prayer and a deeper peace that rests on His grace.
I pray for you now that God will draw you closer as you seek Him, that He will give you grace to know His grace more fully, that He will unite your heart to love and fear Him, and that the peace of God which comes through Jesus Christ will guard your heart and mind. May He hear your sincere prayers and answer with His presence and His peace.