You might try the MOPS (Mothers of Preschooler's) website - mops.org - for devotions for young moms. I have a couple of books I got through them as free membership gifts. One is by Lorilee Craker called
just give me a little piece of quiet - it's hysterical! It has 60 two to three page entries. Not a devotional per say but each one does have a bible verse at the beginning and end. There is also a series of books called little books for busy moms by Cathy Penshorn. The two I have are
Juggling Tasks, Tots, and Time and
If You Ever Needed Friends It's Now. They are chapter books, not devotionals, but the chapters are fairly short and an easy read. I read a chapter a day as a part of my daily devotional time (along with a chapter in the bible and prayer).
Although the examples I just gave you aren't actually devotionals, the MOPS website should have several and most of them should be geared towards moms with young children since that's what MOPS is all about.
My other suggestion would be to check out
Our Daily Bread. It's a non-denominational devotional put out every month by RBC ministries and it's free. There's a short scripture reading and devotion for each day. It's not geared specifically for young moms, but I think they're fantastic (I grew up doing
Our Daily Bread devotions with my family and still get it even today). You can request a free paper copy to be sent to you in the mail each month or just read them online each day at:
http://www.rbc.org/odb/odb.shtml
I hope this helps. Good luck.