I feel for you on the reflux issue. My middle daughter had a pretty mild case and that was miserable enough!
My favorite exercise is always going to be walking. We have a
Safety 1st Two Ways Tandem Stroller that I bought when Linda was about six or eight months old (had a cheaper one before that). Since the front seat flips to face the back seat, they really loved it since they could play together. I'd load them up in that and take them for walks. You could also get a sling or a front carrier like an Infantino (you can find them quite easily at Wal-Mart) and push your older in the stroller and wear the younger.
Of course, it's getting late in the year...If it's too cold where you are to realistically get out and walk, you can try something like yoga. There's a book called
Yoga Mama, Buddha Baby that's specficially about yoga to do with your baby. My oldest, who's 3.5, even got in on the prenatal yoga I was doing, though of course she wasn't too good at it. Pilates will work too, but really walking is the best way to keep your princess held and get your exercise in too. If she'll take being sat down for a little while, you can maybe get some dance DVDs to do with your older daughter (or just play music and dance around); that may well amuse the younger as well.
Welcome, in other words!