You have a DateTime which represents a point in time. And you want to add a number of years/months/days/hours/minutes/seconds to it.
A change in DataTime is not a point, it is a vector (a difference between points). It is really easy to mistake one for the other, as they often have similar structure. However, that kind of type error leads to lots of pain.
Avoiding it doesn't fix your pain, but it makes it manageable.
Adding two DateTime together is adding two points together. Sort of like adding the location of Los Angeles to New York.
Now, adding the "vector" of LA to NY to London makes sense -- because the travel vector is a vector, not a point. And point+vector is just a point.
So this means you need to create a time vector type. A simple time span is an option, but probably not appropriate: because you care about months, years and days, not nanoseconds or absolute time durations.
I'll dub the name of the vector a CalendarVector, as it represents movement on a Calendar, not in time itself.
An easy first pass is to create a tuple of each sub type of time -- years, months, days, etc -- then add them in some arbitrary order to your original DateTime with an overloaded operator+.
You should support:
DateTime = DateTime + CalendarVector
CalendarVector = CalendarVector + CalendarVector
CalendarVector = CalendarVector - CalendarVector
CalendarVector = int * CalendarVector
CalendarVector = - CalendarVector
DateTime = DateTime - CalendarVector
CalendarVector = DateTime - DateTime
ideally. The CalendarVector + DateTime overload is optional, but probably not needed.
However, this only gets you half way.
The big remaining problem is that CalendarVector addition does not commute. Adding 1 month to a DateTime, then adding 1 day, is different than adding 1 day then adding 1 month.
And this is fundamental.
There is the problem of "what does it mean to be 1 month after January 31st", which can be answered, but any reasonable answer to that question doesn't solve the commuting problem.
Your planned constructor -- where you feed it the number of years, months, days, hours, minutes seconds -- is thus ambiguous in what it means.
So a robust solution should not have that constructor.
A solution is to create Years, Months, Days, Hours, Minutes and Seconds types that you explicitly add together. The order they are added together is the order they are applied to the DateTime you add it to. Commuting and "simplification" is avoided until the final application on a DateTime -- so +1 year, +2 days, -1 month, -1 year, -2 days, +1 month is not the zero transformation.
There is a related problem with DateTime-DateTime -- it should return a CalendarVector v such that lhs = rhs + v, but there are multiple such vectors. The same problem can occur with spherical coordinates -- do you mean the short way around the Earth, or the long way? It doesn't matter in some contexts -- but then you halve the result to find the mid-way point. Plus, you get discontinuities as you approach "far side of the world".
So my advice would be to maintain a list of transformations on a DateTime object. 1 year is a transformation that consists of adding 1 to the year field, and then repairing the other fields so they are consistent. These transformations support negation. Addition is applying them one at a time, from left to right. Negation may also reverse the order of application, and adjacent transformations "of the same kind" may combine (so +1 month -1 month becomes the identity transformation, instead of a clamping operation based off next months' end of month), or not (so x = x+1 month,then x = x-1 month on the next line is the same as x = x + 1 month - 1 month).
Yet another approach is to insist that the user provide a policy for what to do in these exceptional circumstances (which happen ... all the time), because this problem is thorny enough that a library that "solves" the problem can at best highlight the problems and force the client programmer to think about them and make decisions.
Add/+function/operator for DateTime has no sense in the way you suggest, because theDateTimetype does not have a neutral value ("zero"). You cannot construct asecondinstance that will provide aMonth=0, so for this way of "adding" a "1 year" will either add 1 year 1 month, or you will need to convert thesecondmanually to "december" (12month) to get a real 1year offset. It gets even more complicated after you notice that there's the same problem with Days, which are not always convertible to simple "31". This is precisely why there's aTimeSpantype