Re: Milk needed during the day/Pumping enough
Mama, please don't beat yourself up! You are doing great and doing the best you can for your little one, so please be proud of yourself! I am also a full-time working mom, whose babies go to daycare. I have a 2 1/2 yo daughter and 4 month old son, and with both children returned to work at 9 weeks.
Don't be afraid to communicate your feelings to the daycare providers. I know it can feel controlling sometimes to tell them how to care for babies when it's their job, but she's your daughter and you still know what's best. They've cared for breastfed babies before, but sometimes need reminding that breast milk is precious and breast fed and formula fed infants are a little different. Let them know that your daughter is exclusively breastfed and that your goal is to continue breastmilk only. Do they give you a sheet at the end of the day detailing her day...what time she slept, what time she ate, how many ounces she took at each feeding. If they are not currently giving you a detailed sheet, then ask them to provide you with that information. That way you can look at her patterns and see if it differs from what you are seeing at home. For example, if they are feeding her less than 2 hours after the last feed maybe it's just for comfort and not hunger. Are they discarding milk that isn't consumed in a feeding? Make them aware that it's okay to keep expressed breast milk that isn't consumed in one feeding to use in the next feeding.
Typically, a breast fed baby will consume 1 oz to 1.5 oz of expressed breast milk per hour while away from mom at daycare, so your daughter would typically be expected to drink 10 to 15 ounces during your 10 hours at work.
You mention that she often is asleep by the time you get home from work. If she is predictably sleeping all evening, then add another pumping session at home before you go to bed, and do this on the weekend too. With my first child, my supply dipped at one point and I started pumping before bed and sometimes awakening early to pump a couple hours before she had her morning feed. Not ideal my mommy's sleep, but it helped increase my supply. I also took Fenugreek supplements with my first child which boosted my supply. Make sure you are staying hydrated...I have a 32 oz water bottle that I fill up 3 times while I'm at work. You might try looking at pictures of your LO while you pump to help stimulate letdown. Do breast massage while you pump to help get more milk. I pump with a Medela PISA and will press the letdown button midway through each pumping session to stimulate a second letdown which helps me get more milk.
Hope that helps! Hang in there!