Daisypond.
I get what you're saying about the post asking for consideration of the whole situation: kids, finances, ex, tiredness. To really think these through, we need more info about the ex. The likelihood is, at his probable age, he'll have relationship (s), and will probably end up inviting his new partner to stay over at the OP's house, or else, how will he have sex with his lover and see her, if he's supervising the kids every evening? Over 3.5 months a fledgling relationship can get more serious, so OP might find children are introduced to Daddy's new partner sooner than they had previously talked about, and then there'll be the issue of this, added to Mum being away. I don't think there is anything wrong with this possibility, not at all, people can work stuff out, but Dad is not going to be a delicate martyr while Mum lives the Loca Vida at an Italian uni, or whatever. But it's a complexity you need to think about in advance and recognise that this trip impacts a lot of lives in the inter-connected community which is them - even grandparents might have to do more, which might be arduous, if one of them has angina and they need to drive over a lot.
It could be Dad is partner in a small business and can't shoulder some of the responsibility because of childcare duties, and other partner starts to resent it, and they split as co-directors sooner than they would have done. 3.5 months is a long time. If the players involved in this are rich, then childcare will be available and helpful, but if they can only draw on family help and paid childcare at times, then a lot falls on him, and I don't think they could do it, if this were the case. Actually, I get a feeling, because OP is confident it could work, that there's leeway built into this set-up, and he is probably the less career-orientated. I say this, as I don't think he would have the kids 50 per cent of the time if he couldn't get them to school easily - he doesn't live near to school. It would be pointless to have them weekday evenings, if he returns home at 8pm, and leaves at 6am for work, and Nanny drives them to school: they might as well just see him at weekends.
It's all about practicalities and whether the ego boost of realising you can study in Italian/Spanish/ German and mixing with like minds, is really a genuine gain in terms of your own spiritual growth.