С методом grid_remove() получилось примерно так:
from tkinter import *
import datetime
def func():
if var_what.get() == 0:
l3.grid_remove()
l3_in.grid_remove()
l1.grid(row=4,column=0)
e1_in.grid(row=5,column=0)
elif var_what.get() == 1:
today = datetime.date.today()
l3_in.config(text=today)
l1.grid_remove()
e1_in.grid_remove()
l3.grid(row=4,column=0)
l3_in.grid(row=5,column=0)
def func1():
pass
win = Tk()
var_what = IntVar()
var_what.set(0)
what_days1 = Radiobutton(text="One",variable=var_what,value=0,command=func)
what_days2 = Radiobutton(text="Two",variable=var_what,value=1,command=func)
l1 = Label(text='Дата1:')
e1_in = Entry(width=10)
l2 = Label(text='Дата2:')
e2_in = Entry(width=10)
l3 = Label(text='Сегодня:')
l3_in = Label(width=10,bg="lightgray")
l_out = Label(width=10,bg="lightgreen")
but = Button(text="Вычислить",command=func1)
what_days1.grid(row=0,column=0,columnspan=2)
what_days2.grid(row=1,column=0,columnspan=2)
Frame(bg='darkgray',width=200,height=5).grid(row=3,column=0,columnspan=2,pady=7)
l1.grid(row=4,column=0)
e1_in.grid(row=5,column=0)
l2.grid(row=4,column=1)
e2_in.grid(row=5,column=1)
but.grid(row=6,column=0,pady=15)
l_out.grid(row=6,column=1)
win.mainloop()