I would say it is not a good idea. I'm pregnant with 2 toddlers as well. I empathize with you so much on this! I'm feeling the same way.
While many of the yoga classes today don't emphasize spiritualality, the pagan roots still remain. Not all yoga positions represent pagan ideas, but many of them do, even if the instructor has learned them being non- spiritual themselves. Part of yoga is the practice of breathing in which many instructors will encourage people to empty their minds and become x, y, z ( I forget exactly what they say).
One might go to the class and just simply ignore that nonsense, but that, I tend to believe, is just falling for a coy trick of the Devil. It's in these seemingly small things that we imagine to be innocent that we give the demonic consent to come on in. By participating in a class built on the foundation of paganism, despite our good intentions, we are opening ourselves up to demonic influence.
My sister used to teach yoga, and she is about as non spiritual as they come. I whole heartedly believe that it is dangerous based on the effects I observed it had on her, but more importantly because at its root, it is not compatible with Catholic belief.
Maybe you would like Pilates, as others have mentioned?
My husband and I recently made a commitment that when there is a little more daylight, we will make time in the evening for me to go on a 45 minute excercize excursion at least 3 times a week, which for me will include brisk walking and stretches before and after. A brisk walk never fails to liven my spirits!
I agree that it's absolutely important that you get out to exercise to help your mind and soul be at it's best, but please don't fall into the yoga trap!