Do you need 6m on a child’s passport to fly to America?

[IHopeYouStepOnALegoPiece]

Read a few different things online and unsure.

Depending on the answer....can you get a same day child's passport renewal

No, you don’t (the US has a special agreement with the UK).
... and no, you can’t get a same day renewal for a child.

No only needs to be valid for the duration of the stay. UK has a special arrangement with the USA.

Here’s a source:
www.cbp.gov/sites/default/files/assets/documents/2017-Dec/Six-Month%20Club%20Update122017.pdf
You don’t need six months on your passport if you are a citizen of one of the countries listed.

Not if it’s a British passport providing it’s valid for the length of stay in the US as the UK is exempt to the 6 month rule:
help.cbp.gov/app/answers/detail/a_id/572/kw/passport%20validity%20to%20enter%20USA/session/L3RpbWUvMTU1NDEzNTU1My9zaWQvdEVrMVg5Ym8%3D
www.cbp.gov/sites/default/files/assets/documents/2017-Dec/Six-Month%20Club%20Update122017.pdf

But as always check with your airline!!

(We had the same panic for DNephews upcoming visit to see us this weekend)

Don't forget your ESTA.

Always look here