Tammy, If at all possible dig up this clump that you got all the buds on and move them where they will get full southern exposure and a little protection from the north wind. South side of a building or fence that is exposed to full sun. Wait until they are about to die down before moving them or mowing off the rest of the clumps. IF weeds and grasses grow over the foliage before they die down it robs the bulbs of the food they would normally produce from the sun that the bulbs need to bloom correctly next year. Plants actually produce their own food from the sunlight. Fertilizers just enhance this food production.
Most daffodils are pretty cold hardy BUT do you know where your Grand Parents lived BEFORE they lived in Pennsylvania? People tend to bring plants and especially bulbs with them as they moved around the world. There are some varieties of bulbs that bloom in the north but won’t bloom down here in Texas and vice versa. Do you happen to have a photo of the daffodil that did open a bloom so that we can try to identify it.
IF it is one of the less cold hardy daffodils then you might have had a hard freeze before the buds had a chance to open killing the bud and preventing it from opening.
By moving one or a couple of the clumps of your family heirloom bulbs to a better location you will see if it is the location or the variety that is affecting the blooming. I expect the size of the clumps is also preventing the bulbs from building up enough food to bloom correctly if ALL twenty buds were in one clump. Send me a picture of the clumps as they are now and then watch in the next couple of weeks as trees leaf out and other plants/weeds grow up around the bulbs and begin to shade the daffodil leaves. If you cannot grow tomato plants in this location and cannot get fruit on tomato plants at this location you probably won’t get many blooms on the daffodils.
NEVER think about moving ALL of the bulbs and replanting in one year. Just divide and move a few clumps at a time. Also consider giving some of these bulbs to some of your friends and ask them to plant your Grandmothers daffodils for you to see if they bloom in a different yard. Keith Kridler Mt. Pleasant, Texas.