You have every reason in the world to worry about your wife showing up with bruises. People do
assume. Many will not ask for clarification. If they do, will she tell them it's BDSM play with someone else or let them think the worst of you?
As a mother, it disturbs me greatly to hear of children crying for their mother while she makes her sexual experiences the priority over them. My older kids are well able to spend a few hours with the younger ones, and I still figure they have to do it often enough when I have to be
at work, that I rarely see my boyfriend unless the kids are with their dad. My boyfriend respects that aspect of my life, me, and my children, and has never once pressured me to leave them for his pleasure.
You say the thought of her packing and leaving you with the kids is scary. If it comes to that, you will find a way. And as things are now, how much is it worth having her 'there' with you when she really isn't actually there, anyway?