Splitting will cut your honey harvest to little or nothing. Who cares about mites if you aren't going to get a harvest. Might as well let the mites have them.
The wording of your comment above could be interpreted as a rather mercenary attitude towards beekeeping: that the objective is primarily to harvest honey, even at the expense of a lost colony from Varroa infestation. Effectively - that the welfare of those animals comes second to the benefits for humans which can be reaped from the bees' efforts.
I understand Brian's last few posts ...
People keep bees for all sorts of reasons: for those with a thousand hives the reasons are clearly those of business, within which one might expect to find a rather hard-hearted approach. But for many, perhaps even the vast majority, with just a couple or half-dozen hives in their backyards - beekeeping is a hobby which may produce a few dozen jars of honey for themselves and friends - but mostly it's a hobby in the same way that fishing (angling), or gardening is a hobby.
Then there's the middle group - the 'sideliners' - those with from (say) twenty to a hundred hives. For such folk I'd suggest beekeeping is somewhere between a self-financing hobby and a way of supplementing an income from elsewhere.
And finally there are the 'odd-balls' (like me), who neither seek an income from bees nor from honey. For some of us, beekeeping provides an opportunity to observe the lives of the most fascinating of wild creatures - one which has intrigued human beings even from before the time of Aristotle. For myself, I now have the opportunity to continue my former occupation of developing new ways of 'building better mousetraps' for the Quality and Assurance Division of a major international chemical company, by trying to improve one or two aspects of beekeeping instead. And for me, improving Quality is the goal, not Quantity.
So most certainly - beekeeping isn't always about achieving a maximum honey crop.
LJ