The standard is - are the claims “patently distinct” from each other.
This is like a 103 obviousness analysis (complicated, arguable and somewhat subjective) and therefore there would not likely be a hard and fast rule one way or the other about elements in separate dependent claims. If there was a rule it might go against your position.
If the widget can be usefully combined with X and the widget can also be usefully combined with Y it might be obvious that it can be usefully used with X and Y at the same time.
And, if the widget can functionally have X and Y together added to it then it might be obvious that either could individually be added to it.
You are free to argue that something about the nature of the widget, X and Y make using them separately and using them together are not obvious from each other.
If the claims were more alike you might get a statutory double patenting rejection that would be worse.
Note - in the first claim the widget is essentially just X + Y and in the second one a widget, by itself, has no X or Y. So the second claim widget isn’t the same widget as the first claim. In my answer I assumed the widgets were the same and therefore that a core widget was a Z, for example.