These are assumptions that it's about control...
How about...
Dad bought daughter a tablet when with him.
Daughter quite rightly wants said tablet set up when with her dad.
Dad sets up tablet as daughter quite rightly wants to use it.
Dad has to set up parental features etc to setup tablet and does so. Being reasonable he also alerts the other parent to the control setup.
That is perfectly normal and how it goes. And indeed how it would go whether separated or not. Whoever sets it up puts in their details.
If the op is convinced this is about control of her, then she either forbids use at her home, buys another or causes ww3 over a tablet she didn't buy! All due to her issues.
And as for those inferring that having this attitude means never having been in a controlling or dv relationship are too talking utter shite, as I certainly have been and guess what disagree with the op.
Yes, there could be a find me type app installed as is quite normal. But given the op won't actually coparebt she'll never know nor have any ability to manage these settings to keep her child safe. Nor does she realise that these features work both ways! And unless connected to WiFi or a network, won't work anyway, so surely the obvious approach would be put on airplane mode of she's really so bothered when out of home? As for the rest, I cannot imagine the father is going to care that much whether it's a Peppa Pig app or YouTube for kids. But has been responsible and reasonable. Not inviting her to join the app would have been unreasonable. As hard as it is, it's time to get over the relationship issues and start coparenting. And putting the children's needs first!