We have a new puppy that we took in from a family who couldn't care for her properly. She was too tiny and they were afraid that they couldn't monitor her needs well ( and she seems to need monitoring

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We've had her a month and she hasn't gained any weight ( she's been seen by the regular vet twice and the ER Vet twice). She was eating well, drinks, very active, sleeps in her crate willingly, pottys well ( formed and regularly) She had one hypoglycemic issue where we took her to the ER. I had given her some Maple syrup to perk her up and the ER Vet said this might have stablized her blood sugar- if it even was an attack ( I was stressed out about this happening)
The family said she is a Yorkie/Poodle cross-breed. Mother a toy poodle ( 7 pounds) and the father a Yorkie ( 5 lbs). The breeder told them to put pure maple syrup on her food if she wasn't eating and to get her over the transition hump. The family gave us the food the breeder was feeding - Diamond Natural- but the adult formula- chicken and rice and we changed it to the Puppy formula same brand. She ate fine.
She was flea/parasite/wormed- twice so far. Vet said she looked fine and healthy. She had the second round of three shots and worming in one day...that was the day I took her to the ER. She recovered. She has since had a flea thing again after the last visit when we worried about parasites cause her no gain. She did have tape worm from the fleas.
She isn't gaining weight, but seems to have grown taller- in her legs. She also looks like she is losing a bit of hair on her legs ( or maybe they are just growing and it hasn't filled in?) She has a big head of hair and a tiny tall body. ( we think she is beautiful but I worry about her eating and gaining). The husband overfeeds our poodle ( a mini who is 20lbs-too overweight ) and gave the new one some people food. Recently. So this isn't the cause of her not gaining although it IS the cause of her new feeding issue.
My tubby poodle will ONLY eat Senior Ceasar ( I know, crap food) with dry kibble out all dayand my husband's table scraps. The little one now eats a bit of Puppy Ceasar that I mix with her Diamond Natural Puppy...but NOW she will only eat it if it has cottage cheese or something human-food in it.
She has had an xray ( we worried she swallowed a battery we found missing- she didn't) and the doc said she looks good on the inside...blood tests fine, everything good. She does have a little dry drandruf and she is itchy- although she has no fleas. Thin hair on the back of her pointy ears...but it's light brown so it looks a bit thinner in that area. Vet isn't concerned about the coat...but gave us Hospital food to mix in ( she hates it). We were only giving her 1/3 packet of Ceasar three times a day...we've upped it to 1/2 and I started adding in the cheese. Maybe I was underfeeding her? She does play AWFULLY hard with our poodle and her toys. Maybe too much?
Any other suggestions? She is adorable and very smart. I worry that she is too tiny...the family told us the breeder said she would be between 5-7 pounds. She is 4 mths and 2 pounds. Is 5 to 7 even possible? What should I be feeding? What about the skin issues...add Olive oil to her food? Bacon grease ( my husband's suggestion- of course!) How much food should she be eating? Maybe I was starving her? She always has dry food out and I've seen her run over and pick a teeny crunchie or two out during the day - though not lately

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Sorry this is so long. I'm a wreck worried about this puppy. Thanks!