How to render custom TextInput or RangeDatePicker instead of common Control

[Estasie]

At my project I need to use RelativeRangeDatePicker with custom input render to have ability change date manually at TextInput field (or at RangeDatePicker - it is much more comfortable with it's mask for date).
I have a problem now, because I can't even enter a number into custom rendered Input.
A simple repro:

Expected result:
I can render different node throw renderControl not loosing it's ux and RelativeRangeDatePicker modal functionality which we see on focus.