* Josiah regularly did the butt-scoot boogie as we liked to call it. He would push himself into a sitting position. (Regularly shows it's his usual form.) Better: He pushed himself. . .
* Even the mocking bird in our neighborhood knew the sounds of our house. We would hear beeps and alarms. (The writer had already established that as a regular occurrence.) We heard. . .
* I’d get up in the morning like every other mother and take my son to school and to the tennis courts at the nearby park. After three sets of doubles, I’d hop in the car and I'd head to Macys. (I'd means I would and the writer established customary behavior with the first word. In the final clause, it should read, I hopped. . .I headed.)
Would as a helping verb establishes usual behavior.
You need to use it only once.