Given the large size of the flag it would be extremely difficult to properly mount and frame it in a case or frame. About 4 years ago I donated an old 38 star American flag to the city of Marshfield and had it framed. The flag was about 3' x 5' and that is about the max you can do with a standard frame without having to reinforce it. I was also forced to use plexiglass instead of glass to keep the weight down. Otherwise the frame just wouldn't be able to support it. The cost is not cheap for something like this...it ran me about $300 (just for the framing)!!
You can hire a professional conservationist to sew up and preserve damaged areas of the flag but it may take you awhile to find somebody and I'm not sure what something like that would run.
As for the D-Day museum or other museums in general...the contract is pretty much standard procedure. Museums just don't have the space to display all of their collections and usually just a fraction is on display at any given time. However, some museums are good about rotating their collections on a regular basis. The Wisconsin Veterans Museum located in Madison is like this. They have some wonderful items on display from the Civil war onwards and rotate displays, but some of the real "goodies" are kept in storage under climate control like all of the Wisconsin Civil War regimental battle flags from the Civil War. If you wanna see those babies you'll have to make a special appointment with the curator!
Another thing to keep in mind is that these Nazi flags and banners are still somewhat easy to obtain and aren't really considered "rare" by most militaria dealers. You can obtain some through military antiques dealers and even ebay (although they aren't supposed to sell them on ebay) for anywhere from $200-$500 depending on size and condition. I would venture to guess that the D-Day museum (and most other well-known museums out there) already have several of these flags/banners in their collection which have been donated over the years.
My advise to her would be to hire somebody to conserve it and keep it in the family as a reminder to future generations what her husband did during the war as a member of the "greatest generation." As long as it is kept in a cool, dry place and out of direct sunlight...it should last for generations to come.
John