If deer are hungry enough -- no other food supply -- they will eat plants that they normally wouldn't touch. The fact that the doe has fawns with her indicates that she isn't leaving them alone so that she can go forage for food.

Typically the doe leaves the fawns, hidden in foliage, during the day while she ventures out for food. She must not have a good place to leave them, or she must not have a good milk supply and is already taking them out to forage with her. I assume that the fawns still have spots? That's young to be taking them around.

Deer resistant gardening is my thing and I have been watching the deer habits for years.

A mother doe is also usually accompanied by other females. Those other females will often act as babysitters. I always see one or two other females present when a doe is giving birth. My local herd tends to have their fawns in a grassy opening in the woods behind my porch, so I witness this several times every June.

The fact that your doe and fawns are alone and out and about foraging typically unpalatable food is unusual. The wild food supply must be very, very scarce and this family sounds like they are isolated from a larger herd.

The deer think my yard is the all you can eat salad bar..always a problem..I just get rid of what they eat and do mass planting of what they wont.