Although this exact scenario no longer applies to the reader who sent me the question, I was nevertheless intrigued by the situation because it seems like a near-perfect storm of complex personal situations that can arise during the negotiation stage of a faculty hire. Consider:
Some of us have been in the situation of getting an offer of a faculty position and then having to bring up the fact that our spouse is also searching for an academic position and would it be possible to hire a second person as well? In some cases, the two-body problem is common knowledge throughout the process, and in some cases it is news to the hiring department.
And some of us have been in the situation of getting an offer and then at some point needing to bring up the fact that we are going to give birth just before or soon after starting our new faculty position.
I was in both situations, but consecutively. When my husband and I were hired at our current university, there was a gap of about 3 months between signing the contracts and my calling up the department head to have an "Oh, by the way.." conversation. He was very nice about it, mentioned that other faculty had young children, and emphasized that the department was family-friendly. I had been very nervous about calling him, but everything turned out fine.
But what if you are in both situations at once? When and how do you communicate about these issues with the department head or other administrators?
My advice is to bring up the spouse situation soon after getting the offer if you are going to be asking for some sort of second position. That is necessarily going to be part of your negotiations and decision.
Issues involving parenthood, however, are not typically part of the negotiations, although I know some faculty and administrators who have circumvented the long waiting list at on-campus childcare centers by making guaranteed childcare a part of the negotiations. Unless there is some practical reason why you need to announce your parental status, however, I don't think you should bring it up if you aren't comfortable doing so and if it is not relevant to the negotiations.
Some women feel that it is deceptive not to mention it at an early stage, including before the contract is signed. If you are going to ask for family leave or tenure clock stoppage very soon after arriving, administrators would certainly want to know this as soon as possible, but it is not deceptive if you wait to convey the information.
That would be my preference, but only because it makes sense to me to separate 'things that are relevant to the negotiations' from 'things that are not'. What I don't know is whether or how making an early announcement of pregnancy (i.e., before the contract is signed) might affect the negotiations. Could it weaken your negotiating position?
Or am I wrong that it is in fact useful information at the negotiating stage, and, if you have a family-friendly department head, you can work out an amenable arrangement re. teaching (for example) proactively, as part of your hiring?
If you have any direct or indirect experience with needing to tell your new department "By the way, I'm in the family way..", I hope you will share your story and note (1) when you told, (2) why you decided to tell when you did, and (3) how things went.