I agree that she is trying to manipulate you into accepting a situation which will be crushing for you but will enable her to have things entirely her way. You do not have to put up with this - in fact, I would seriously question her claims to still love you if she is trying to create a situation which is so utterly centred upon herself. She appears to be thinking only of her short-term desires to have it all, and not of the devastating impact on you and your children.
You do NOT have to put up with this, you really don't. Things are raw at the moment, but as SGB says, over time (and it will be a long time) things will get better, and even become manageable.
You need to get as much support as you can - do you have male and female friends in RL who you can confide in? Both sexes can provide you with support in different ways, so it will help you enormously if you can start to corral your friends' help.
You also need to ask yourself why you are willing to consider an arrangement which would be so detrimental to your well-being. I'm sure part of the reason is that at the moment you're still in the shock phase and so are unable to think as clearly as you need right now - that's perfectly normal and you may need some time in this phase before you can start to make decisions. In fact, I think you should tell your wife in no uncertain terms that you're not in a position to make decisions right now, and that since she is the one who has betrayed you, now she has to just wait for you to gather your strength/ thoughts/ resources before you can start to make decisions for the future.
Then, when you are able to start thinking about the future, Picture yourself in this domestic set-up which your wife has suggested, in 1, 5, 10 years' time or more - what do you see? How does it affect you? Is it a picture that you want to become a reality? I sort of know a man who allowed his wife to manipulate him excessively before, during and post divorce, and it is not a happy picture. She is also as manipulative towards their children, and he is not able to challenge this, so she is totally in control of everyone, and everyone is miserable when she's around. This has been going on for years - is that what you want for yourself and your children?
Huge sympathy to you, Rubarb.