I don't think your MIL is right, I definitely felt movements when in labour with DD, actually the fact that I could feel (and see) movements helped me stop the consultant from breaking my waters as the machine wasn't recording the movements properly.
But rather than take advice from me (or MIL!) just call your MW or labour ward and see what they say.
Contractions feel different for everyone. For me, they were an all-consuming pain that came in waves and felt especially painful across the bottom front of my bump. Like period pains, but in waves and more intense.
What you have sound more like pelvic pain. My dd was breech until 36 weeks, and she kicked, pushed and stretched all around my pelvis (whereas ds, who was cephalic, caned my ribs!)
Call your midwife and get checked out if you're not sure.