You should be able to monitor the tablet as the main caretaker. Children at a huge risk online. It's anything from cyberbullying, to accidentally coming across abusive porn (yes, I know the vast majority of porn is violent and abusive, but I put it for clarification), to being stalked, to being targeted by pedophiles, to gambling and gaming addictions.
It is good a child learns their way around in the digital world, but they absolutely need supervision. There are two things you can do and both have already been mentioned here.
It's her tablet right? You ex gave it to her? So I would personally just factory reset it or have it done at a repair shop and set it up so you can monitor it yourself with a new Google account for her.
Or you give the tablet back to you ex.
Personally I think the first is the best option, because otherwise she will use it at his house unmonitored. If he kicks up a fuss, just give the tablet back to him.
Furthermore, I think it would be wise to get another Google account for yourself as well and don't tell him about it. He can email you on the old account and you can use the new account for everything else.