My husband is still in the U.S. with us, and he will not fly over to the UK till early September. I will be submitting my spousal application before he leaves, so I will not have any evidence to submit that supports a separation (again, because husband is still in U.S. with us).
Yep, in that case, you just provide the evidence of living together in the US. You only need to provide evidence while separated, if you have been apart for a period of time before applying.
I wonder if I should include our child's passport photo? You confirmed birth certificate is not necessary, but do we need to show that our child has a valid passport?
Nope, you don't need to do either.
As a UK citizen, your child is completely irrelevant to your visa application and you do not need to provide any documents relating to them.
It's your responsibility to make sure your child has a valid UK passport - it makes no difference to UKVI... all they are concerned with is your circumstances, because you are the one needing a visa.