This is a tough one for the crew too, I'm sure the mother was giving them a very difficult time.

Here's the UA bassinet policy:

A limited number of bassinets can be reserved for use, free of charge, on international aircraft only. Bassinets are available for customers traveling international segments in United BusinessFirst® on select 757, 767, 777 and 787 aircraft and in United Economy® on 747, 757, 767, 777 and 787 aircraft. Bassinets are not available for customers traveling in United Global FirstSM, United First® or United Business® at this time.

Bassinets are large enough to hold an infant weighing 22 pounds (10 kg) or less. They may not be used during taxi, takeoff or landing, or when the seatbelt sign is illuminated. Along with bassinet requests, we will provide accompanying seat assignments for an adult traveling with an infant and up to one travel companion. Call the United Customer Contact Center at 1-800-UNITED-1 (1-800-864-8331) within the United States, or call the appropriate Worldwide Contact Center. There will be no fee for these seat assignments when arranged by the United Customer Contact Center or with a United representative at the airport. Bassinet availability is limited, so we recommend that customers call ahead of time to make these arrangements.

Note that they don't have to pay for the E+ seats. But there is no right to bump a pax from an existing seat assignment.