Although the wording around claiming the Childcare Access & Relief from Expenses credit can be confusing, if you have a spouse, you must check the box that says your spouse is the "supporting person".
The credit is claimed by the lower-income earner, and failure to check the box saying your spouse is the supporting person results in an incorrect calculation based only on the lower-income earner's income, not the "combined family income".
Depending on which version of TurboTax you are using (Online or the CD/Download version), the screens to make this claim may appear different. As long as you check off that your spouse is the supporting person, your claim calculation should be correct. And you check to make sure it is by looking at your Provincial Summary page.