I think you still love your wife, you have withdrawn because you are hurt by her comments (and who wouldn't be)
Once a week sex is better than most and certainly fine for most busy families. You may fancy her in the mornings, but she is going to hate that with the dc about to wake up at any moment. I know I would.
I have a few suggestions for you:
Get the photo album out and look at your lives together, this never fails to pull at the heart strings and reminds you of everything you both have.
Remind yourself that you will lose every day contact with your children, family house and life as you know it if you don't make every effort to fix this. So do everything you can to save your marriage whilst you still can.
Suggest a hobby you can do together so that you are spending time being intimate and together without sex. It seems like this is a pressure to her
When you are feeling sexy, why not massage her, or gently kiss her with tenderness, have a bath together and do things differently. If she likes the lights off, respect that, light a small candle.
Don't expect her to be sexually adventurous when she is knackered and tired for much of the time, save those times for holidays and time when she is more recharged and feeling well.
Readjust your expectations of her. Look at her, talk to her, cuddle her when she is tired. It is not all about sex.
Ask her what you can do to be more interesting to her, maybe switch your wardrobe, get fit and show her there is still the spark there.
Go to a theme park just the two of you, start doing fun date nights I think you miss the lighthearted days when you could be carefree (but no one is carefree with young children if they are doing a proper job of parenting)
Try sex counselling, and if you can't find that in your area then pay for it. Maybe it will help...
Can you actually imagine leaving your young family just because your sex life isn't what it used to be, and your arguing? It is not much of a good reason in my book.
I would try everything to fix this. Your marriage is worth fighting for. Every marriage has its ups and downs, and sometimes you just need to ride it out and stand by your young family. There is no such thing as a perfect marriage.