I have no where near the time constraints you do, but what I've found is if I can get an entire quilt cut, and the pieces organized, you can make progress by sewing in 15-30 minute chunks. Maybe you can arrange a family member to come over for a couple hours and baby sit while you cut a quilt.
I agree with the poster, they are little for such a short time!

Everyone had such great ideas. Now that I'm a great grandma I look back and miss those days, reading together, playing games together - I missed so much just keeping them fed, housed, schooled and paying for all of it. Enjoy your time with her -- the scrap box will work, also those pictures with the holes on the edges with the cord you sew along will be good when she gets a bit older. I'm a big fan of pizza boxes for each project, with all the pieces cut out you can accomplish a lot in 20 minutes or go all the way and set your timer for 30 min. I use the timer, it gives me a deadline - I don't get side tracked with the timer. ADD (i'm convinced I have it) without the timer, my mind goes elswhere and before I know it, I'm hunting fabric from my stash for another project and another box. LOL Happy stitching.

I'm retired now, but I can well remember feeling like you feel when my three children were growing up. It seems like yesterday. I fixed up a sewing box for my kids like Hillcountrygal suggested. I included fabric scraps, yarn, lace, a doll, and round tip scissors for them to "sew" with. With the tv on that occupied their interest while I sewed a little. Just enjoy each stage of your child's life as much as you can. Time passes quickly.

I watch my grandson during the day and I can't go into my studio without him following and wanting to get into everything. I seem to only be able to work on quilts on the weekends if I am in the mood to do so. Meanwhile I am working on a counted cross stitch project in the living room while he plays. I know how you feel. My three adult children were young once and I felt the same way you do now.

I wish I lived close to you. I would cut some projects out for you to do in your spare time. I was in your shoes and burned the candle at both ends to find time to sew. Of course back then I could exist on a few hours of sleep.

A friend once told me to give myself 15 minutes a day for sewing - it's amazing what you can get done in a short amount of time if you do it consistently. I found it to be very relaxing.

Nancy Zieman's book 10-20-30 Minutes to Quilt is what got me started quilting. My kids were older by that time, but we home-schooled and I worked part time at our church and I didn't think I had time to sew. It takes a little prep work and organizing but it will amaze you what you can accomplish in those little short bursts of time. I was so inspired after the first one that I kept on going and haven't stopped. And I agree with the others, cherish the time with your daughter. It may be annoying at times, but who knows, maybe spending time with you "sewing" will foster an interest that will last a lifetime. I have taught both my girls to sew and they knew they were always welcome in my sewing room (except the few weeks before Christmas when it became Santa's workshop). They are grown now and both have retained an interest in sewing. My oldest even made her first quilted table runner for a shower gift recently. I treasure the memories of the times I spent "creating" with them even when it seemed like they were under foot.

I sometimes get up 15 minutes early and just sew. I like to sew scrappy blocks in this small time frame, so it is easy peasy, no thinking, no measuring. Just sewing. I love the strip blocks or crumb blocks for this. Log cabin would be another good one. 10 minute block is awesome for this also. I find I can do one or two blocks each day, very rewarding! It is hard when your busy with children and normal life day to days things, I didn't sew as much those days either. The children are only little for a short time, those were the best years as my dad told me. He was right. I miss those days. Even today, it sometimes is difficult to find uninterrupted time to sew. Perhaps a weekend sewing retreat might be a great treat or gift to yourself.

I remember those days...when I felt like I would never be able to sew again. They will pass, and you will get time again. Does your husband know how much you really would like some time for that? My husband was very good at trying to take our boys for outings almost every weekend so I could have a few hours for myself.\They got to do some fun stuff, and I got the time I needed for myself. Sometimes I would sew, sometimes I would just take a nap. I hope you can get some time to sew!