No, the program is correct at allowing a $1200 credit.
From the 2441 Instructions:
If you paid qualified expenses for the care of two or more qualifying
persons, the applicable dollar limit is $6,000. This limit doesn't need
to be divided equally. For example, if you paid and incurred $2,500 of
qualified expenses for the care of one qualifying person and $3,500 for
the care of another qualifying person, you can use the total, $6,000, to
figure the credit.
To qualify for the credit, you must have one or more qualifying
persons. You should show the expenses for each child in column (c) of
line 2. However, it is possible a qualifying child could have no
expenses and a second child could have expenses exceeding $3,000. You
should list -0- for the one child and the actual amount for the second
child. The $6,000 limit would still be used to compute your credit
unless you have already excluded or deducted, in Part III, certain
dependent care benefits paid to you (or on your behalf) by your
employer.
https://www.irs.gov/instructions/i2441#idm140680692399504
