If she is still eating something plus haylage/hay she is probably not so bad that you need to do something right now (may be famous last words), and getting some twin lamb drench in the morning should be fine.
Yes having read quite a bit on milk fever, I am with fsmnutter on dropping the Alfalfa down, as Peter Dunn (in Goatkeepers veterinary book) also describes why. (as fsmnutter describes too)
Also - giving her a shot of Calciject is not causing any more harm, and may just give her the Calcium boost she needs - a goat(or sheep) that is lethargic and doesn't want to stand at this stage of pregnancy is most likely to be short of Ca (and energy) and therefore weak. Stress of any kind can also cause milk fever, so a fight/disagreement, you may not even have seen it?
I don't know what could be wrong with her kids, but the high temp is pointing to some kind of infection/inflammation in her system. Giving the dam ABs/AIs is really all you can do at this stage for the kids.
Is she a 1st kidder - their udders often are enormous quite a while before they kid, in comparison to older nannies who only "fill up" a day or so before they are due. That is definitely my experience. Unless the udder is hot/sore and possibly leaking I wouldn't touch it - if you do take milk off at this stage I would freeze, although I don't know when the nanny starts to make actual colostrum. If you do open up the teat canal now I would recommend to use a teat dip (or just a good antibacterial spray or iodine dip you use for kids' cords) to make sure you don't end up getting an infection/mastitis as dirt gets in when she sits/lies on her udder.
Sorry probably not much help here... an it's getting late. my brain is kind of gone to sleep...