Emergency Broadband Program

Does anyone know if undocumented immigrants with citizen children qualify for the federal emergency broadband program?

No it’s a federal benefit

He asked a simple question. He did not ask for your moral judgments.
No one cares about your moral values.

The answer is probably yes. An undocumented with U.S Citizen children should qualify if their household falls under the economic criteria of the program.
The following info comes from the program itself:

Who Is Eligible for the Emergency Broadband Benefit Program?

A household is eligible if a member of the household meets one of the criteria below:
(The keyword is "one" of the criteria. That's all you need. Just one of these factors and you qualify)

Has an income that is at or below 135% of the Federal Poverty Guidelines or participates in certain assistance programs, such as SNAP, Medicaid, or Lifeline;
Approved to receive benefits under the free and reduced-price school lunch program or the school breakfast program, including through the USDA Community Eligibility Provision in the 2019-2020, 2020-2021, or 2021-2022 school year;
Received a Federal Pell Grant during the current award year;
Experienced a substantial loss of income due to job loss or furlough since February 29, 2020 and the household had a total income in 2020 at or below $99,000 for single filers and $198,000 for joint filers; or
Meets the eligibility criteria for a participating provider's existing low-income or COVID-19 program.

Source
https://www.fcc.gov/broadbandbenefit

Thank you to everyone that actually took the time to answer OP's question. If this thread spirals again, permanent bans will be issued.