I went riding while I was pregnant with Yasin before my bump was showing but I took it easy and I love riding so I was fairly confident of my ability to saty on a quiet horse.
I think that you should stick to doing what you're comfortable with. Your SIL obviously has a differant comfort zone than you and its knid of insensitive of her to try and push you into her zone.
Its great to get some excercise while you're pregnant but you should stick to the options that aren't going to stress you out. I found that a round of golf was a nice gentle option for excercise when I was pregnant.
Your SIL isn't quite correct that there is nothing you can do that can lead to miscarriage - a blow to the stomach would definately hurt bubs and it could casue placental abruption. Raised body temperatures can also cause problems.