My Child is a high school student in NY taking 2 college classes. Does this qualify her for the NY college tuition expense credit?

No.

Normally a High School student taking college classes is not enrolled in the college which is a requirement of the New York Credit. 

You are entitled to this credit or deduction if:

• you were a full-year New York State resident;
• you, your spouse, or dependent (for whom you have taken an exemption) were an undergraduate student who was enrolled at or attended an institution of higher education and paid qualified college tuition expenses; and
• the student is not claimed as a dependent on another person's tax return.

Thank you for the reply.  We received 1098-T forms which is why I am wondering. 

The rule in question was:  ...undergraduate student who was enrolled at or attended an institution of higher education and paid qualified college tuition expenses. If this is true, then you would qualify for the credit. There are some scenarios where the high school students don't qualify, but some do and yours might be one!