Hi A.,
I think it's a great gift you are giving to your friend to let her move in with you. It's so hard for single moms when they find themselves in a situation like this.
I think that your ex husband is right to be concerned about this. But I think that just being aware of the situation might be enough. I don't recommend the sleeping arrangements that you said you were planning. I would keep one upstairs and one downstairs. And not allow them to share a bathroom.
It's very normal for kids to be curious at this age and I think that you should not put them in situations where they can explore in this way.
I'm not saying that you are putting them in a situation like that, but just that in every hour of the day, you will need to be aware and have an eye on them. Just the fact that you are moving in together will spark their interest.
When I was younger, I thought that the kids were completely uninterested in this kind of stuff and my boys loved playing with the nextdoor neighbor girls. I felt like all their activities were very well supervised but found out later that they had opportunities to explore each other. It blew my mind and I wasn't quite sure how to handle it, but it happened even under my close watching eye.
So all this to say - Don't think that just because they are well supervised that things can't happen. They are curious and will continue to get more and more curious as they get older. You may think you know your children well and they don't seem interested, but I think you (like me) will be very surprised.
Good luck with this!