The Hardest Condolences
There's a tradition that says you shouldn't invite people to a bris because you don't want to put anyone in the position of having to say no to doing a mitzvah. It's a mitzvah to welcome a new baby into the world, and it's a mitzvah to comfort mourners. The former is easier and implicates you in sharing happiness instead of sorrow. Easier certainly doesn't equal more important, though. You could make the argument that it's unfair of your friend to have brought this tragedy to your attention when it wasn't clear if you would be in a position to provide comfort, but life can be unfair, as your former supervisor has now experienced all too painfully.
You might not have anything you want to say to her. You might think she'll resent hearing from you. You might feel like it's weird to get in touch now because you've been out of touch for so long. You might worry that she'll think it's out of place. You might even resent being put in a position to think about how you'd feel if you were in her shoes because, well, it's just unspeakable to consider. Your hesitation to comfort her because of your own child is both self-centered and completely understandable, but you're overthinking the situation. When someone is suffering, you comfort them, even if you're not entirely sure how much comfort your words can actually provide.
Realistically, nothing you say will make her pain go away, but you can let her know she's not alone. Perhaps hearing from you from a somewhat distant part of her life will provide a positive connection to a time prior to this tragedy. She may or may not be Jewish, but regardless, you can consider the sentiment of the traditional Jewish words to say to a mourner: "May God console you among the other mourners of Zion and Jerusalem." Yes, the individual is mourning, but there is a communal context that allows someone at their darkest moment to know that others before them and among them have survived and moved on with life. A very helpful article on mourning from myjewishlearning.com  says the following about these words: "Jewish tradition understands the quandary of those who want to comfort mourners but cannot articulate words of comfort, so it provides a formulaic religious response to what is essentially an inexpressible emotion."
Send her a card. It can be simple. It can just say, "Thinking of you." It's the right thing to do both for her and for you. We can hope that our collective futures include more opportunities to welcome babies into the world then to mourn for those who have left. If you hear about this woman having another baby, maybe even having a bris, send a card then, too.