I'm really sorry OP. This situation sucks and it's so unfair that as the wronged party you have to hold all those feeling in and be calm and reasonable and do the right thing, while at the same time, losing your kids 50% of the time. And all because your wife has done something monumentally selfish. It's galling to then have your kids see only the best of her, even if that's ultimately best for them, it's still gutting for you
I think too many posters are treating you as if you are the one automatically in the wrong, because you are male and as women,have been in the receiving end.
The only advice I can give you is to say that every time you let your kids see the positive in their mum and hold back the natural bitterness, you are being a better parent and putting them first. They may or may not come to see that in time, but you are doing what a good parent should do, which is to put them first.
The only other thing I can say is to try and build yourself a new life and not think about her at all - let her be wiped from existence as far as you are concerned. Tell mutual friends that you don't want to hear about her at all.
Finally, see a solicitor - if you've been a sahd, she might have left you up shit creek financially. 50/50 usually means neither of you pays child support since you both have to house the kids, but I'd revisit this agreement if her provision isn't the same quality as yours (ie kids have bedrooms, not sleeping in living room etc). And she may owe you spousal support or a more generous financial settlement if you've sacrificed earning potential to provide childcare.
Not letting her stiff you in the divorce settlement will go some way towards making you feel better.
Best of luck