Most OBs do not recommend a fast-induced labor. I think the biggest Shayla is 9 Av (except when Nidche). I've heard so many different Psakim.
I've never heard of a Chiyuv for a pregannt woman to fast on a minor fast in the 2nd or 3rd trimester, and virtually all Poskim would say a pregnant woman should start Y"K and switch to Shiurim if feeling weak.