Veterans' Access to Child Care Act (Sec. 2) This bill directs the Department of Veterans Affairs (VA) to provide child care assistance to an eligible veteran for any period that the veteran: (1) receives covered health care services at a VA facility, and (2) is required to travel to and return from such facility for the receipt of such services. The bill defines: (1) "covered health care services" to mean regular mental health care services, intensive mental health care services, or such other intensive health care services to which the VA determines that provision of child care assistance would improve the veteran's access; and (2) "eligible veteran" as a veteran who is the primary caretaker of a child and who is receiving covered health care services from the VA or who is in need of, and who would receive, such services from the VA but for lack of child care. Included among child care assistance to be provided under this bill are: a stipend for the payment of the full cost of child care offered by a licensed child care center, which shall be modeled after the VA's Child Care Subsidy Program; direct provision of child care at an on-site VA facility; a payment made directly to a private child care agency; and collaboration with a facility or program of another federal department or agency. (Sec. 3) The bill extends through September 30, 2026, the $90 monthly limit on a VA pension paid to veterans residing in nursing homes when their nursing costs are paid through title XIX (Medicaid) of the Social Security Act. (Sec. 4) The bill extends through December 31, 2024, VA authority to collect funding fees for certain VA, VA-guaranteed, or VA-insured housing loans.