Are you using mySQL? I'm only familiar with MS SQL Server so take what I say with a grain of salt.
Try using square brackets around your column name like this: [First_Guard_Last] - or fully qualify it like this [Parents].[First_Guard_Last]
Also, since I'm not familiar with mySQL, I did some googling for you and came across this (see the synatx under section 3.1) - http://sql-info.de/en/mysql/referential-integrity.html
and this: http://dev.mysql.com/doc/refman/5.0/en/alter-table.html
Are you sure your synatx is right?
From what I read in the 2nd link, it seems to me that your syntax should be:
ALTER TABLE parents MODIFY First_Guard_Last varchar2(15) not null
Toward the end of that 2nd link, there are a bunch of forum posts. One says:
You can't drop a NOT NULL constraint on a column the way you can a foreign key or an index, or a default. Instead, just use the 'change' or 'modify' syntax and leave off the NOT NULL bit:
alter table table_name modify col_name bigint default null;
Any pre-existing indexes or foreign keys on the column are not affected.
Hope that helps!