I would hate to be out and about looking after a toddler for the first time. It's much easier to contain them in a home. I would allow her to stay home but build it up before then. After all, it's quite possible your Mum may be required to babysit for hours on end while you give birth to your second. In the weeks leading up to the scan, I would drop DS over to your Mums and go out for 10-15min, and build it up from there.