HELP trailer sway almost killed us!

If nothing else, when you pick the trailer up from the shop, drive on the interstate to see how it does and see if the sway returns, if you see small bits of it that worry you, put 3 or 4, 5 gallon water cans in the front of the trailer or if possible add some weight (battery, water whatever) to the tongue and watch for changes from that.
Level and a need for additional tongue weights are likely the issues after the brakes are fixed.