Unity: Without falling into criticism or argument, how does one best request help when over-extended or physically / mentally overwhelmed?
Firstly, let's excise the second part. The making of a request is what it is, regardless of whether I am over-extended or overwhelmed. If the request is valid, it is valid. If it is not, it is not. If the request is reasonable and realistic, that is what it is. The method is the same in relaxed circumstances as in fraught.
Now, let's examine the situation. If one person is regularly over-extended / overwhelmed, and the other is not, the reason might be an unfair distribution of domestic or family duties. The remedy in such situations is not to open the emergency valve, although that might be necessary on occasion, but to have a more serious discussion, when the immediate emergency has passed, about who does what.
Sometimes one person is over-extended or overwhelmed not because of an unfair distribution of domestic or family duties but because their own life is over-packed or they are occupying themselves with excessively trivial matters. The other person, under such circumstances, is under no moral obligation to bail out the over-ambition or triviality of our protagonist. The feeling of being over-extended or overwhelmed is not a signal of the importance of the activities in question.
When a request is to be made, make it politely, by saying, 'I need your help. Could you please ...?' Very simple. No explanation. If they want an explanation, you can give it, although frankly that should not be needed, if the person's judgement is trusted. If they argue, don't argue back. If they say 'no', that's that. Simply get on with the day and let the chips fall. I don't repeat requests unless (a) the task can be done only by the other person and (b) some time has passed to allow them to take action.
If the other person is habitually unreasonable, then I don't know what the remedy is. I have never successfully changed another person's personality, turned a selfish person into a selfless one, or turned an unreasonable, irrational person into a reasonable, rational one.
A note about the language: criticism or argument are not 'fallen into'. They are actively decided upon. If one, rightly, does not wish to criticise or argue, then don't.