Oh no, Lisa! Could you offer her a four day a week job and put DS2 into a childminder on say Mondays. She could still come over and do whatever her morning routine is (get him dressed, fed, etc.) then she could have the whole day off and you or DH could pick him up from childminder in the evening. That would cut her hours down to basically four days, give her some time to do her own stuff. But, on the other four days she needs to really keep up with x, y, and z.
This of course assumes that there is one day where the other kids are in full time school.
As for laptop, take it with you in the morning. Just say you put some work on it last night and you need to take to work with you today.
Or... just be honest. "I know you've been looking at jobs on gumtree. If you are unhappy I'd rather you told me why and maybe we can work something out where you can be happy. DS is really attached to you and I don't want to lose you, but this laundry over here and those toys over there are the reason I wmploy a nanny so they do need to be done on a daily basis." Or something like that.
BTW, my nanny works 12+ hours every day. But, she is live in and doesn't have any kids. So I guess that makes it a bit easier.