indexing by windows with step gap over a pandas DF

My df is datestamp index. I need to split it in two different df with fixed window (for exemple 2 day) in alternation like this:

df1 = yellow ans df2 the white

Thank so much for your help

Assuming the following example input:

import pandas as pd
import numpy as np

df = pd.DataFrame({'date': pd.date_range('2021-01-01', '2021-01-14'),
                   'value': np.random.randint(0, 100, size=14)
                  })

If you have a range index, you could use it to compute a group and split:

out = dict(list(df.groupby(df.index//2%2)))

output:

>>> out[0]
         date  value
0  2021-01-01      5
1  2021-01-02     35
4  2021-01-05     25
5  2021-01-06     59
8  2021-01-09     32
9  2021-01-10     44
12 2021-01-13     22
13 2021-01-14      6

>>> out[1]
         date  value
2  2021-01-03     36
3  2021-01-04     97
6  2021-01-07     10
7  2021-01-08     57
10 2021-01-11     31
11 2021-01-12     28