I like the Omni in Woodley Park. My friends have stayed there and liked it. I live in Woodley Park and sometimes walk out back - they have very nice grounds. Big lawn in back and a fountain. Also overlooks Rock Creek Park (separated by a fence).
Walking distance to Zoo which will be good for your Mom. 4 month old won't care.
If your Mom is in good shape, she could also take the 1.5 mile walk up to the National Cathedral. It costs now to get in, but I found Cathedrals great for babies because they are looking up at stained glass windows. Mine liked it.
And if she is in good shape, she can walk to Dumbarton Oaks (surprisingly good fall foliage views from up there).
http://www.omnihotels.com/hotels/washington-dc-shoreham