Sure, I can write a test case generator for the problem statement you've provided. Here is the Python code for the test case generator:

```python
import random

def tcgen():
    A = random.randint(-10**9, 10**9)
    B = random.randint(-10**9, 10**9)
    
    # Ensure A != B
    while A == B:
        B = random.randint(-10**9, 10**9)
    
    V = random.randint(1, 10**9)
    W = random.randint(1, 10**9)
    T = random.randint(1, 10**9)

    return A, V, B, W, T

# Example of generating a test case
A, V, B, W, T = tcgen()
print(f"{A} {V}")
print(f"{B} {W}")
print(f"{T}")
```

### Explanation of the Code:
1. **A and B**: These are the coordinates of the two children. They are randomly generated between -10^9 and 10^9, ensuring that `A` is not equal to `B`.
2. **V and W**: These represent the distances that "it" and the other child can travel per second, respectively. They are randomly generated between 1 and 10^9.
3. **T**: This represents the number of seconds within which "it" must catch the other child. It is randomly generated between 1 and 10^9.

### Sample Output:
The generator will output values formatted as in the problem statement. Here is an example run:

```
-1000000000 999999999
1000000000 1
5000000
```

This output represents:
1. The "it" child's starting coordinate is `-1000000000` and can travel `999999999` units per second.
2. The other child's starting coordinate is `1000000000` and can travel `1` unit per second.
3. The time limit is `5000000` seconds.

Feel free to run the test case generator multiple times to get different test cases for your problem!