I read somewhere that this was an early idea that didn't get used--that being pregnant with the twins gave her temporary access to their midichlorians. And I doubt this was what they were thinking, but--with TWO ultra-force sensitive in her, she might be even more powerful than Anakin, though of course completely untrained.
Maybe she seeks out help to get training, just to cope until she gives birth. She couldn't admit the situation to Yoda or the council, but Anakin would of course be around, and Obi-Wan might be safe to trust if Anakin is away.... and maybe she starts having her own visions of the future, and now has the power to do something about it.
Pregnant Padmé has force powers
Maybe she seeks out help to get training, just to cope until she gives birth. She couldn't admit the situation to Yoda or the council, but Anakin would of course be around, and Obi-Wan might be safe to trust if Anakin is away.... and maybe she starts having her own visions of the future, and now has the power to do something about it.