Hi Fishy
As a vet and long time lamber, hopefully I can help.
Sounds like the second lamb had been dead for a while, I usually find if they come out within the sack, especially if it is brown coloured, they died in the womb some time ago.
Sometimes these have died because of some infection, occasionally a knock or something, it can be very hard to know what caused it, and if you only have a small number (up to 1-2% of lambs) then it is usually not even worth testing for infectious causes.
As regards a placenta, it is fairly common for the placenta to be retained if there is a problem at birth, such as malpresentations, hard pulling or dead lambs. Normally the placenta comes away within hours, but if they are retained, then bacteria come in and gradually break the afterbirth away from the uterus. This will be smelly, but it should come away on its own at about 3-4 days after lambing. The betamox usually covers for 2-4 days, so as long as she remains bright and eating, then I would just watch her over the next few days. Pulling the afterbirth usually will not help as the deepest bits are likely to still be attached, so just wait and see. If she goes off colour, or it is beyond 4 days after lambing, it may be worth getting the vet to have a look, or repeat the betamox yourself and see how she does.
Hope that helps
Suzanne