My sister-in-law (who is trustee of the family trust) said, in response to our wishing to start the process of selling the house (which is part of the family trust): "I do not believe anything can be done before April 28 at the earliest. That's when the 120 days is up since notification of the trust to all the potential beneficiaries; the time in which any challenge can be made."
My wife and I have some health issues that need us to move as quickly as possible on liquidating the assets in the house (currently, our primary residence), in order that we are then able to buy our own place.
It seems to me that the trustee sister mistaken about having to wait the 120 days, when all (3) of the sisters have no challenges (to my knowledge) and have expressed their desire to do what they can to help us move on with our lives.
I'd like to inform the trustee sister, that she's mistaken and that it's all right for her to now engage a Realtor and sell this house.

It's impossible to help you on this without knowing precisley how the trust documents are worded. Do the trust documents specifically require a 120 waiting period? Perhaps an option to consider would be for each of the beneficiaries to provide a signed and notarized document to the trustee that waives their right to the 120 period and authorizes the sale process to commence immediately.

I believe it was the trust lawyer who devised the 120 day period. I don't believe the trust document itself mentioned such a period (I do have a copy of the trust, if I need to reread it).