Oh I'm no Supernanny! I've just been there, seen it, got the eye-bags . I may sound calm now, but oh you could have scraped me up off the floor with a teaspoon then - I felt so useless, bad-mummyish, and knackered.
About the comfort-and-return, you don't need to leave the baby crying for long. I couldn't bear to do the 5,10,20 minutes, so I did 30sec, 1min, 2min, and so on, and always returned if I felt ds's crying was getting too upset. He's not aware of the time, only of his distress.
No doubt that's why it took me a bit longer than expected before ds learned to self-settle contentedly, but OTOH maybe he's just a stubborn little tyke (yup, he is!).
I know it's a drag implementing a super-strict routine when you're by nature a more easy-going type, and miserable to get home and not get a chance to play with your LOs, but this is an investment of probably not more than 1 month to get the most marvelous pay-off. And once sleep has been sorted, you'll find that there can be some flexiblility.
Remember that you two are doing a good job, doing the best for both your dd's and for yourselves as a couple and as a family. It's a tough business, parenting on no sleep.
Tell you what, why don't you skip the argument, agree with dh that you're both knackered, both wrong, both need a drink and a cuddle, and curl up together for some sleep?