No DO (or MD) schools in the US require inorganic chemistry. However, they all require general/intro chemistry.
While some school may call their intro chem course inorganic - it really is a misnomer - inorganic chemistry is a seperate branch of chemistry and in most major universities, inorganic chemistry is an upper level chemistry course along with pchem, anal chem, orgo, biochem, etc. Calling general chemistry inorganic chemistry because some topics of inorganic is covered in gen chem is almost analogous to calling intro biology "molecular genetics" because you covered DNA, RNA, histones, etc. in the intro class.
I doubt your wife dealt with point groups, symmetry elements, group theory, characterization table, irreducible representation, MO and LGO theory, crystal and lattice structures, etc. that is commonly found in syllabus of most "intro" inorganic chemistry class. It really is a shame that her school called her gen chem class "inorganic" (note the blame is on her school, not on her)
Here are some syllabus of "inorganic chemistry" classes - as you can see, it is not general chemistry,
http://www.cmu.edu/mcs/van-outreach/gfw_inorgchem_p3_syllabus2.htm
http://chem.unk.edu/chem430/syllabus02s.html
http://www.lycoming.edu/chem/spring2005/333syl.htm
http://web.chemistry.gatech.edu/~wilkinson/Class_notes/spring_2000_1311_web_page/syllabus.html
http://www.jsu.edu/depart/pes/chemistry/gryko/syllabi/cy311.html
Anyway, for the OP - inorganic chem is not required by any medical school in the US. At least 1 year of gen chem + lab is required though.