Another post on sleeping "through the night!"

Our daughter is 13 months and typically goes to sleep between 6:30 and 7 p.m. She has milk before bed, but we put her in her sleep spot still awake, and most nights, she is ok, rubs her eyes and falls asleep shortly thereafter. Some nights she awakes after about an hour and needs some TLC and sometimes milk to fall back to sleep. 

She has slept all the way through until 6 or 6:30 in the morning on several occasions, but never consistently, and there is no singular factor that has determined it. Once asleep, she sleeps until anywhere between 1:30 and 4:30.  She wakes up and you hear: "eh, eh, eh".  Not really crying, but complaining.  I have waited to let this pass, but it persists, and generally rises in intensity, at which point I take her out of the crib, feed her and change her diaper.  She then will be awake for anywhere between 1/2 hour and 1 1/2 hours.  She falls asleep next to me in the bed (will NOT go back in her crib) and wakes anywhere between 5:30 and 7:30 thereafter, depending on her initial wake up time and when she was able to fall back asleep.  Because she has been up for so long overnight, she is still exhausted when she wakes up in the morning and struggles to make it through until 10 a.m. That is usually 1 1/2 to 2 1/2 hours.  She is tired throughout the rest of the day, but, since dropping her second nap about a month ago, will not take another, and so the cycle continues. We have tried a gentle cry it out and the "no cry sleep solution", but neither one seems to do anything to alter the middle of the night waking or the length of time she will be up afterwards.
 How this is impacting our life: Because of our daughter's exhaustion level, she becomes fussier, and so even when she is awake during the day, it's not that much "fun!"(though whoever uses that word in conjunction with parenting has never had kids, IMO). Because she is ready for her nap no later than 10, it makes getting out of the house before 1 next to impossible, and leaves us without storytime options etc. in the early part of the day, as these all start at 10 or 10:30. The ability to get out in the early part of the day and then once more in the afternoon was *huge* for me with my first child and combatted the isolation of childrearing.

In addition, I rarely fall back asleep after the middle of the night waking, and I am getting more and more worn down (I am no spring chicken!), prone to illness and stress, etc. There is no possibility of going to bed earlier for me (I do most of my own "work" from 8-10 p.m. and 4:30-6:30 a.m.), so that is not an option. But I am so tired, in a perpetual brain fog, and just becoming increasingly depressed about it all. I see a therapist and a psychiatrist, but I would not say that I am clinically depressed, just seemingly crushed by life circumstances!
 I know from having an older child that this too shall pass, but we were blessed with a much easier road in many ways with our first, and so it all felt as if it went by really quickly. Everybody said that the second would pass even more quickly, but I am finding the opposite to be true, and running out of steam and stamina. Any words of wisdom or concrete suggestions would be lovely. Thank you!