Modern Reformation ran a good article by a mom of two younglings about feeling like a second-class Christian. I'm sorry it's not available on-line without an account, but I think a summary may still be helpful.
Moms' days are filled with sippy cups, bottles, diapers, Elmo, crayons, chores, church activities, and occasional moments of coveted nap-time solitude. Their individual spiritual practices? Let's just say they don't involve hours spent alone under the trees with their Bible.
How can they stay spiritually healthy, much less grow in grace, without quiet time and the spiritual disciplines?
Conventional advice recommends two or three minutes of Bible reading, a little bit of journaling, a snatch of prayer, etc. All helpful suggestions. But something really big is missing from this counsel and much of evangelicalism.
Here's the key question, who is responsible for sanctification? Ultimately it's not up to us. Self-betterment has nothing to do with sanctification, even when the attempts are to better ourselves spiritually.
Thus sanctification is not a work you undertake through various methods and disciplines, but an amazing act of God's grace. You simply turn to him in your brokenness and receive from him the treasure of grace. This is fundamentally different from believing that it is up to you to cultivate spiritual growth through the faithful practice of spiritual disciplines.
So, if it's not ultimately up to you to assure your own growth in Christ, then how do you grow spiritually? Do you just sit around waiting for God to do something?
When we look to the early church members' own practice, they "devoted themselves to the apostles' teaching and to the fellowship, to the breaking of bread and to prayer" (Acts 2:42). In other words, they listened to the Word preached in fellowship with other believers and reflected on it; they made it a priority to be there when the church celebrated the Lord's Supper; and they were consistent in prayer-not just on their own, but with other believers.
These are the "means of grace"--the places where we can expect God to meet us, and the manner in which we know he will sanctify us. Your spiritual life is shaped by meeting with God in the presence of his people and hearing the Word preached by someone set apart to preach it.
You are not sentenced to second-class status in the Kingdom of God because you are a busy mom. The Lord is faithful and he has promised to complete the work he began in you (Phil. 1:6).