I think that First Lady Madison's practical and yet noble nature compelled her to find the breaking of the frame to be acceptable. In her letters, Madison is revealed as one who understands the urgency of the situation. She is also one who is shown to understand the symbolic importance of the preservation of the defining elements in the new nation's history. It is for these reasons that she was fine with breaking the frame. In all likelihood, the frame did not have a glass cover; it was the wooden frame itself that was broken:
Our kind friend, Mr. Carroll, has come to hasten my departure, and in a very bad humor with me, because I insist on waiting until the large picture of General Washington is secured, and it requires to be unscrewed from the wall. This process was found too tedious for these perilous moments; I have ordered the frame to be broken, and the canvas taken out. It is done! and the precious portrait placed in the hands of two gentlemen of New York, for safe keeping.
This excerpt reveals some fundamental truths about the First Lady. The use of "these perilous moments" shows how important the instant is for Madison. She recognizes that there is imminent danger approaching the White House. She fully grasps what has to be done in order to avert this threat. The "process" being "tedious" also reveals how she would find the breaking of the frame a necessary risks. When she "ordered the frame to be broken" and "the canvas taken out," it is clear that Madison's challenges with breaking the frame were overcome in the understanding of what needed to be done at that particular moment, at that defining instant. It is shown to be as much her crucible as it was the nation's.