It's just really hard, it goes against all your instincts to let them go when they are ill.
But I think it's good that he said he would take them anyway, he's sticking to the 50/50 and in time you'll come to terms with it even though it does seem ridiculously unfair now seeing as he blew up the relationship. It's beyond hard to accept that.
I think, in the nicest way, it's also good that the children were unwell so soon into the arrangement with his mum - it's easy to think you can look after children when they are well, and the weathers good etc. Whole different ball game when they are ill, and you already suspect it won't work with her long term, so it might be good if that comes to a head sooner rather than later.
Step back, text only, this is just another "first" you have to navigate, next time will be easier. Hugs x