Should out daughter claim herself as a dependent? We made too much to be able to claim he tuition/education expenses. She works part time and made over $15000.

No, not necessarily. Remember, as a student your daughter's earnings do not matter. The key word here is "qualify". If you the parent "qualify" to claim the student as a dependent (and I bet you do) then the student has no choice but to select the option for "I can be claimed on someone else's tax return". It doesn't matter if you claim your student or not either.

Basically, the parent has a choice to claim or not to claim, and the student has no choice and must select the option for "I can be claimed...."

"We made too much to be able to claim he tuition/education expenses."

You still claim her has your dependent if you qualify. Then your daughter will claim all the education stuff on her tax return. She won't get nearly the credits you would if your income was under the threshold. But she'll get a little bit, I'm sure.