I am not 100% sure that it is normal to see grey stools, but almost 99% sure it is - in her case. I think all children are fussy when it comes to having vegetables, but to have a child reject fruit is highly unusual. Is she still feeding from a bottle? If so, you must first stop using a feeding bottle to give her liquids/milk. Secondly, why not keep trying new fruits like figs, tomatoes (technically it is a fruit, you know, :-)), pine-apples, peaches, plums, cherries, mangoes, or even good old banana ...? Another suggestion would be to try and use peanut butter and to use whole wheat bread instead of white sliced bread. Tofu would have more fibre than cheese, and you can try oats as they have good fibre too. Last but not the least, why not give her dry fruit like dried figs, dates, prunes, raisins, almonds ... they are all fibre rich and will soon resolve her constipation
Take care. If the constipation becomes too bad and she starts getting pain because of the non-passage of the stools, you must see her pediatrician
immediately. He may recommend professional evacuation of her bowels before suggesting any further medication.
With best regards,