Non-rev travel with infant under 2

Hello! My wife and I are flying from the UK to US, for the first time as non-revenue d3 (a relative works for AA).

We also have an infant under 2 who we are happy to have stay in our lap. We have non-rev two tickets for us and have been told that we just need to inform the staff at the desk on the day about the infant.

Just want to check if this is correct?

We are hoping to bring a child pushchair and car seat - my understanding is that this should be ok as well? (assuming we are allocated seats)

Any advice is appreciated! Thanks.