D.A.
Hi M.,
Your state of exhaustion is so similar to what mine was. I have a 4 1/2 and almost 3 year old. My 4 year old still has never slept an entire night through. I thought I was a healthy eater too but I had no idea that I wasn't even close to feeding my body properly. I became a personal wellness coach and learned a TON about nutrition - I now have enough energy to not only keep up with my toddlers but I no longer need the coffee I was drinking almost all day long. I can give you more information if you are interested - feel free to contact me.
Your question about caffeine - I would not up your caffeine intake while breastfeeding your daughter. I would start by making sure that your body is getting approximately 100 grams of protein a day and every 2 - 3 hours you should be having a little "something" to eat. Your best boost of energy will be if you can snack on things that combine protein and complex carbs (lean turkey and a piece of fruit or some vegie sticks, cottage cheese with fruit, etc.) By eating every few hours you will be giving your body natural energy and it will help to better sustain you through your day. Also make sure you eat within 45 minutes of getting up - you need to give your body some energy first thing in the morning so it sets the tone for your day.
As I said my 4 year old is not a great sleeper either - she not only doesn't stay asleep but it was impossible to get her to sleep - I did start giving her a VERY small dose of melatonin before bed - it helps her body to calm down just enough for her to get to sleep.
Hope some of this helps - I would be happy to talk to you more about what I learned if you want to contact me.
Good luck - D.