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Yes, one option would be to author a model or script tool that has 2 data-time parameters and based on use input executes some logic. Then from a button in your add-in you could launch that tool. GP Tools have 100's of parameter types that allow you to build a UI for accepting user input and built-in and customize-able validation that can be run before the tool is actually executed.
Another option would be to build a .Net add-in. The .Net framework offers a rich environment for building windows forms that can accept user input and execute code. If you would prefer to author your form in .Net you could still have you business logic in a python script tool and call the tool from .Net passing in any required parameters.