A sentence should at least contain subject and verb.
For example: I sleep => I = Subject, Sleep = Verb
I walk on the street => I = Subject, walk= verb
For 1st sentence you mentioned:
her and me (wrong, should be "She and I", her and me are "object")
no verb, at is not a verb
I suggest you may change the sentence as follows:
She and I eat breakfast at my coffee table.
For 2nd sentence:
no subject
and I do not get your meaning about "sleep in our eyes"
I suggest you may change the sentence as follows:
I watched my baby daughter sleeping comfortably in her tiny bed.