Sure, I'll create a test case generator for the "Frog's Straight Path Home" problem. Here's the generator code which will randomly create valid test cases based on the provided problem constraints:

```python
import random

def frog_path_tcgen():
    # D is the distance to the nest (1 ≤ D ≤ 10000)
    D = random.randint(1, 10000)
    
    # L is the distance the frog can jump with a big jump (2 ≤ L ≤ 10000)
    L = random.randint(2, 10000)
    
    return D, L

# Function to print the generated test case in the required format
def print_test_case(D, L):
    print(f"{D} {L}")

# Generate a test case and print it
D, L = frog_path_tcgen()
print_test_case(D, L)
```

This generator will create random test cases for the problem while adhering to the constraints specified:

- \(D\) is the distance to the nest, generated randomly between 1 and 10000.
- \(L\) is the distance the frog can jump with a big jump, generated randomly between 2 and 10000.

Here's an example of how you might use this generator in a script:

```python
if __name__ == "__main__":
    # Generate a single test case
    D, L = frog_path_tcgen()
    print_test_case(D, L)
```

You can run this script to generate random test cases for the "Frog's Straight Path Home" problem. Each run will produce a different test case within the given constraints.