Hi Berry,
I've had 2 c/secs. With both, I drove about 10 days after. Definitely check with your insurance. My OB told me that the risk is not being able to respond quickly in an emergency braking situation.
Ask your doctor too, but I think the most important thing is to follow your instincts about how much you need to protect your body for a good recovery. In other words, if you're given the all clear to drive, but still feel exhausted/unnerved or have any qualms, then don't.
The toddler lifting issue is so hard. I found it heartbreaking. With both mine, dh was off work for 2 weeks after and gave the toddler lots of attention, which they LOVED. I was comfortable sitting in a chair and hugging, or bending down to give attention.
Near the end of pregnancy, I suggest telling dd that Mummy needs her help and she can't carry all the time. Most toddlers transition well to being offered an arm/hand for leverage in & out of the car. Use lots of encouraging words, "Can YOU do it? Wow, you are getting to be such a big girl." When they want to be picked up & carried, sometimes it helps to make it into a little chasing game--"Can you catch me? I think I can get to the front door before you!" It doesn't mean you have to move fast, just making funny feet movements and doing it with a sense of fun is usually enough. If you start doing this before baby arrives, then it will be a bit easier.
After the first 2-3 weeks, if you are recovering well, you should be able to pick her up occasionally. HTH.