Can we take the required post 70 1/2 IRA distribution entirely out of my IRA which is larger and leave my wife's IRA alone for this tax year?

No, that is not permitted.  IRAs are accounts owned by individuals.  Each individual must separately satisfy their own RMD by taking distributions from their own accounts.

However, if your wife if not 70 1/2 years of age yet and HAS NOT started taking the required minimum distribution (RMD) then she is not compelled to take a distribution this year. If like "superuser" has indicated she has started her RMD last year or earlier, then she will have to take another RMD again this year.

I interpreted the question as asking if wife's RMD could be satisfied by a distribution from husband's IRA, and the answer to that is No.

So did I.

Fair enough!