I want to know the average of a Mother's first child when her second
child is born.  This obviously does not include any Moms who just have
one child.  I am also not concerned with 3rd, 4th, etc... children at
this time.  Please provide source of data.

Mother avg age for first birth in US 2003 census is 25.2
http://www.census.gov/Press-Release/www/releases/archives/facts_for_features_special_editions/006560.html

Avg age differential between 1st and 2nd born in families that ONLY
have 2 children is 4.
See page 44 of this study from 2004:
http://www2.gsb.columbia.edu/divisions/finance/seminars/micro/fall_04/Black.pdf

Would it follow then that the avg age of the mother at the birth of
the 2nd child would be 25.2 + 4 = 29.2?

Thanks, however I think I may have not worded the question properly. 
I know the average age of a mom when she has her first child, and you
are correct at 25.2 as of 2003.  What I want to know is:  How old is
the average Mom's first born child when she has her second child? 
Yes, obviously you can add the 2 together to get Moms age.

4 years old is not the correct answer.  I expect that it is some
number between 19 months old and 35 months old, I just want to know
exactly what it is.

Thanks

Here is data from 2000:
Average mother's age for first birth: 24.9
Average mother's age for second birth: 27.7
That would make the first born kid an average of 2.8 years (31 months).

http://www.cdc.gov/nchs/data/nvsr/nvsr51/nvsr51_01.pdf

Unfortunately this is mildly old data and it doesn't remove data from
mothers who only have 1 child.  My guess would be that mothers who
have multiple children are likely to start younger than mothers with
only 1 child, so if anything the average age of the first born kid
would be slightly higher than the above calculation.
Also, between 1994 and 2000 the average age increased about .4 years
and the age has been slowly rising since the 70s.  So it would not be
a horrible assumption to guess that the average age from 2000 to 2006
increased about the same.