Hi Abrigham....Congratulations on your confirmation.
An Intention we make during Lent is a private devotional intention we make with the Lord. Our Lord who knows everything about us and understands our hearts, also does know and understand you brought LIFE into this world, and brought a soul with that life into this world that will be raised to know and worship Him. He also knows all the work (AND lack of sleep) entailed with that and understands when our Intentions fall short of our best made plans. Not being able to fulfill a private devotional promise is not a sin. It is a matter of prayer you can have with the Lord, and maybe you will want to try to continue the readings as you can, or considering how busy you are you may want to change to another devotional intention that better fits your schedule with baby.
I do recommend Jimmy Akin's website for his information about Lent. It answers this question you have posted, and many others as well about Lent and devotional promises.
Our Lord does so understand the intentions of our hearts, and does understand how our time is filled with babies, and jobs, and cooking, and cleaning....maybe as you are busy, you can lift up in prayer whatever you are dong for baby with the intention of doing that for the Glory of God (and any other private devotion you wish).
I went through something similar this Spring. I had the intention of reading the Bible every day during this Year of Faith. Then a few things changed that have me planning music, practicing music, reading the General Instruction of Roman Missal, studying Chant, and Latin....and with all that I've not kept up with my Bible Readings as I had planned.
One other thing, what you are doing right now as mother to your baby, is the most important job, vocation, occupation, this world knows. You are the "hand that rocks the cradle", shapes and forms that child's life and thus you have the greatest opportunity to change the world. Of course you want to incorporate some type of devotional that also enriches your soul (and mind) that fits your schedule, but try not to be too hard on yourself about this.
May God Bless you and your family.