Roman shades on very wide windows sometimes have issues with the just the weight of the shade also what do you want from the window covering . I think light control can be handles better with solar shades one on each window that give light and heat control with keeping the view and since this is a playroom there really is no need for nightime privacy.

If you're able to do inside mount, I'd do one for each window, regardless of what kind of shade you use. If it has to be outside mount, then I think one wide one would look nicest, especially since it's a bay. If looks don't matter, then you could put two on one headrail if possible, for minimum gap between the two.

It looks like your window is bowed? - I’d do individual inside mount shades :)