I am not entirely clear what "backup care" is supposed to be. From my reading of the instructions, if the employer provides care for you (including emergency care when your circumstances warrant, maybe that is "backup care"?) the fair market value of that care is reported in box 10.
Here are the W-2 instructions for box 10.
Box 10—Dependent care benefits (not applicable to Forms W-2AS, W-2CM, W-2GU, or W-2VI). Show the total dependent care benefits under a dependent care assistance program (section 129) paid or incurred by you for your employee. Include the fair market value (FMV) of care in a daycare facility provided or sponsored by you for your employee and amounts paid or incurred for dependent care assistance in a section 125 (cafeteria) plan. Report all amounts paid or incurred (regardless of any employee forfeitures), including those in excess of the $5,000 exclusion. This may include (a) the FMV of benefits provided in kind by the employer, (b) an amount paid directly to a daycare facility by the employer or reimbursed to the employee to subsidize the benefit, or (c) benefits from the pretax contributions made by the employee under a section 125 dependent care flexible spending account. Include any amounts over your plan’s exclusion in boxes 1, 3, and 5. For more information, see Pub. 15-B.
Publication 15-B is here.
https://www.irs.gov/pub/irs-prior/p15b--2025.pdf
The employer must have a dependent care assistance program (DCAP) that is in writing and applies to all employees. In this case, they can exclude up to $5000 of FMV of care assistance from your taxable wages. If they don't have a written DCAP, or they have a program that only applies to some employees, then the assistance is considered taxable wages and is reported in both box 1 and box 10 (they can't play favorites with tax-free benefits).
Then looking at the instructions for form 2441 on the employer benefit side, the instructions for line 12 say,
Part III. Dependent Care Benefits
Line 12
Enter the total amount of dependent care benefits you received in 2025. Amounts you received as an employee should be shown in box 10 of your Form(s) W-2; however, don’t include amounts reported in box 10 that exceed your plan's exclusion and are therefore reported as wages in box 1 of Form(s) W-2. If you were self-employed or a partner, include amounts you received under a dependent care assistance program from your sole proprietorship or partnership.
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I don't know the details of your arrangement so I can't tell you exactly how to apply these rules to your facts.
It may be that your backup care benefits should be tax-free and should have been excluded from box 1. In that case you need a corrected W-2 from your employer.
However, it could also be that your employer plan for some reason is not allowed to be tax-free. In that case, your entry on form 2441 should only report the portion of box 10 that represents tax-free benefits and should not report the amount also included in box 1. (And in that case, save your documentation because the IRS may send a letter asking why form 2441 reports less benefit than box 10.)
If that is the case, one possible workaround is to edit your W-2s to only report the non-taxable part of box 10 (the part that is not included in box 1). Which I guess would mean $0 for you and $1909 for your spouse. but be prepared to answer an IRS letter. As part of gathering the documentation to support your filing method, I would get something in writing from the employer explaining why the backup care is considered taxable and why they won't issue a corrected W-2.