Your puppy does need to be on puppy food. Have you tried the Royal Canin Yorkshire Puppy kibble?
Sometimes you have to let them skip a meal or two keeping in mind that you should monitor them for hypoglycemia;BUT, in saying that, most puppies of her age won't have a drop in blood sugar like that unless there is something medical going on.
You may have to do a bit of tough love here within reason.
Once they know you will keep giving other options they will often refuse food just to get you to give something different.
Yes, some are pickier than others. That I do know but I would not try to give her a home cooked meal without consulting with a vet nutritionist but that is pricey. There is a website, run by a vet nutritionist where you can do that, but you must by the supplements if you want it to be balanced. The diet is free.
www.balanceit.com
Good luck!