J.L.
Each child is different, all I can offer is my experience from my daughter who was born at 30 weeks and had similar eating troubles. When babies 1st start on solid foods, their digestive system needs time to adjust too, it's hard sometimes, but try to be patient.
She was on an acid reflux medicine, that did not help much.
She is my oldest & 6 yrs old now. She was never ever able to drink a full 8oz bottle of milk or formula at one time. She is perfectly healthy & has a healthy appetite, it will come in time.
The latest information I know is; solid foods should start about 6 months for breast fed babies, but 4 months old for formula fed babies). Basic order....in general yellow first with rice & oat grains, orange and pale green next with barley & wheat grains(1-2 months after started solid foods), then dark green & red last(about 10+ months of age) ***citrus fruits, corn & melon are exceptions to this color rule & should go at the after 10 month age
I did the same with the cereal rice in the bottle, oat to eat). I did not mix foods at 1st (let her eat the cereal, then the fruit after or veggie after...she'd eat the cereal from being hungry, then eat more of the fruit/veggie because of the taste. Not at 1st, this took several days.
The fruits seemed too sweet for her, she did better with the 1st veggies instead of fruits (1st fruits=applesauce, pears, ripe bananas, 1st veggies=acorn squash, butternut squash, sweet potatoes)
When I switched to making my own food instead of storebought, that also helped her reflux & digestion out (the storebought jarred food tended to be sweeter & more watery than I prepared). That was harder to start, but once I started freezing it in ice cube trays to have handy 1oz servings, my feeding time went better; either heated up in a coffee mug or could let thaw in a leftover/washed baby food jar. I also started earlier feeding her 3 times a day, trying to make lunch the larger meal for food, and also giving her more bottles at nighttime (like a 4 oz bottle every 45 min to 1-1/2 hrs apart a few hrs before bedtime....think of it like a snack before dinner, then fed her food for dinner with a bottle, then a bedtime snack or dessert).
Night time, well that was the hardest for me, it took more time, but I knew 'I' had to do suffer though it for the longer term benefit. No one had any suggestions for me, this is just what I decided to do; When she woke up, I would tell her it's not time to eat yet, and give her a pacifier. I would stay near her & comfort & reassure her, but repeat that it wasnt time to eat yet. Each night I would wait a little longer before feeding her, finally she got used to it. I was tired for awhile, but I am sure not near as long had I not done it, and it wasn't too long after she actually started sleeping through the night.
As she grew, she still needed a 'snack' before bedtime to help her sleep better.
It was a long time however (several years) that she started eating larger portions. Her stomach was just not large enough to handle more at 1 sitting. Some people are just made that way (I know I wish I could shrink my stomach to be that way...lol)
Oh yeah, and playing with her A LOT before & after dinner and getting her outside in the evening whenever possible to get her nice & tired helped for nightime too.
Sorry, I tend to be long-winded, I just hope something in my little dissertation might help :-). I can feel for you as you are tired & get frustrated, but just try to stay patient, this will pass & one day they will sleep through the night (so you can wake up in fright to make sure they are okay). Best of luck!