It's normal deer behavior, for the fawns to stay close to where the mother died. Feeling bad about it, is only labeling some sort of unnecessary guilt trip on yourself.
A mature doe is going to push her fawns away to get bred, during the rut. A breeding buck will kill any fawns that interfere with his breeding of the mature doe. Therefore, the reason why she pushes them away. It's nature's way.
The reason I say this is:
2 years ago, on opening day of our Archery Deer Season, I was walking on a 2 track path when I noticed a white belly ahead of me. As I checked her out, it was a mature doe with its' hips crushed/injured from a vehicle accident. This was approximately 175 yards from a State Route. I intended to remove her later, cause she died about 25 yards from my treestand.
I went ahead and climbed my tree and waited for first light. Shortly after first light, her 2 fawns showed up and circled the area, bedded down and hung out for the next 3 1/2 hours.
As soon as they left, I got down, went to get my deer cart, came back and loaded her up. I hauled her about 200 yards to the north and dumped her in a creek. This kept varmints from the area and didn't interfere with deer travels from the rotting carcass.
I continued to see the fawns throughout the remaining months of the season.