I Love exercise and I think it is really important to move your body throughout pregnancy and labor. The general rule of thumb is not to start working out while pregnant or do more when pregnant than you did before pregnancy. Seeing a personal trainer that specializes in perinatal care/support is really beneficial, but what I would recommend more than a trainer is a pelvic floor specialist, especially in the third trimester.
Squats while working out can yield some great results, I personally really like doing them, maybe not on the day after, but I like the results. But in pregnancy, especially in the third trimester, we do not what to overbuild the muscles of our pelvic floor. In labor your vaginal muscles really need to be able to relax and get out of the way so that a baby can come down and out. Women who are big into lifting, cross-fit and other intense exercise routines can have a really hard time getting that baby out because their pelvic floor is so incredibly strong.
Seeing a pelvic floor specialist can help you identify how to relax your vaginal muscles and what exercise you can do to help build the correct muscles for delivery. I think a really good exercise to begin in the second and third trimester is prenatal yoga. You can stretch the muscles and create strength without building a ton of muscle.
Now when you are in labor, squats are an incredible tool to bring baby down. If you have a doula they may suggest doing squats during contractions, it won't be fun, but oh so effective.
Because it can be hard to hold the position in a contraction like the image above, you can ask your partner, doula or nurse to hold your arms in front and support your weight and then have someone behind you doing a double hip squeeze, that will bring the baby down like a champ. This the time I like to see squats, this is when it really helps you see your baby faster.
Once you are cleared to exercise again, then start up that squat routine with weights if you want, I hope you see the results you want!