Customer is disputing over 2k on her debit card. Claims her toddler used her phone to make the charges to google play. Are we responsible?

She essentially gave her access device to the toddler, so no.

Regardless of whether the toddler was handed the device or picked it up, a parent is liable for the acts of their children so I say no as well.

Reg E is not as black and white as this. In this example, the parent had their access device saved on a mobile application and gave the access device to the child, so the parent is liable as the transactions do not meet the definition of an unauthorized EFT under 1005.2(m). However, if a 16-year-old minor steals mom's debit card and makes several unauthorized purchases, the bank is going to be liable because the parent did not give authority to the minor to use the access device.