I am sorry to hear that the 2nd pregnancy is getting complicated. Actually--I want to assure you that really all the news is good--1) 37 weeks is considered "term" (I had a baby at 36 and one at 38 and both are very (VERY) active healthy boys. Sometimes P/E occurs much earlier and that is scary for everyone. At 37 weeks--you can expect that the baby will not likely need to be in the NICU, and will be able to come home with you.
2) She is in the hospital. This is where she should be if she has proteinuria and elevated BP. She may be induced soon--if they talk about giving steroid shots--then they are planning to deliver.
3) Her BP is coming down. I don't know if she is on medication in the hospital, or if she is just on bedrest but that is good news--if that changes (if the BP goes back up, or her proteinuria goes back up) expect her to be induced. They may go straight for a c-section if all goes haywire--which unfortunately, with this disease, can happen. That is why it is great that she is in the hospital.
4) She has you--and you are asking all the right questions and looking for moral support. You will be amazed what a difference that will make for you--and then by extension her. She needs to know that you are there and will ask the questions that need to be asked. Not that you would--but if her doctors want to deliver early--I would not argue. Ask, absolutely, why, but trust that they want to keep her pregnant as long as possible--but at this point--depending on how the disease is progressing, it is best to be safer. Safer with preeclampsia oftentimes means delivering the baby.
Let us know how everything is going. Also-0--check out the English group Action on Pre-eclampsia (APEC). They have a great support network there and if you are English, (I am just assuming because of the nhs.uk reference) you can call for support and advice. We have their link on our Links page.