The memorial also would have its back to the Lyndon B. Johnson Department of Education Building, which sends the wrong message because Eisenhower and Johnson accomplished much together, the family wrote.
Memorial planners have said the tapestries will be transparent and won't block views of the building.
The family also questions the sustainability of the metal material and who would keep the woven metal clean of leaves and trash caught by the tapestry.
"Great monuments to our leaders are simple in design and made of durable stone for a reason," the family wrote.
The debate comes as families take a stronger role in national memorials. Martin Luther King Jr.'s children and late wife helped shape the new King Memorial.
In the 1990s, Roosevelt's family was divided over how a disabled president should be portrayed. A statue of Roosevelt in a wheelchair was eventually added.
The influence from families emerged with the Oklahoma City bombing memorial and more recently with the 9/11 Memorial in New York City, said Kirk Savage, author of "Monument Wars: Washington, D.C., the National Mall, and the Transformation of the Memorial Landscape."
Representing Eisenhower as a teenage boy, as Gehry proposed, would be interesting, Savage said, because it makes people relate to him in a different way, perhaps more closely.
"It's about humanizing the leader, bringing him down into our space and our world, so that we can engage with him," Savage said. "If they had just decided to do a statue of him in a military uniform or as president, in a way it wouldn't have provoked any commentary at all.
"No one would have really paid attention."
Davis Buckley, an architect who has designed other memorials in Washington, said a more daring approach with Eisenhower's memorial makes sense because "Ike" established the basis "for who we are now in the 21st century." Many people may forget that he integrated schools and created and the Federal Aviation Administration.
"He was a visionary, and I think that it is appropriate to push the design envelope in terms of what this memorial is," Buckley said. "It's a question of how they get there."
Susan Eisenhower said the family is trying to be constructive and ensure there is a full public discussion.
"We knew him better than anybody," she said. "I just don't feel any part of him in this."
Eisenhower Memorial Commission: http://eisenhowermemorial.org
Brett Zongker can be reached at http://twitter.com/DCArtBeat
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