Thank you for the encouragement. I will ponder these things.
Brother, I did have an experience and an insight this past Lord's Day which may help you further.
We had the Lord's Table this week. We sit down at an actual table and pass around bread and wine. My daughters are 3.5 and 20 months respectively, so we must seat them with us when we go up, and we've really got no other practical choice (they do not partake). My older daughter was a distraction most of the time because of her playfulness and tendency to test boundaries. The observation at the Table itself wasn't profitable. I admit I was sinfully angry. However, that doesn't mean the observance was a waste.
Here is WLC 175 on what we are to do after the Lord's Supper, my emphasis on the part most relevant for me that day:
Q. 175.
What is the duty of Christians, after they have received the sacrament of the Lord's supper?
A. The duty of Christians, after they have received the sacrament of the Lord's supper, is seriously to consider how they have behaved themselves therein, and with what success; if they find quickening and comfort, to bless God for it, beg the continuance of it, watch against relapses, fulfill their vows, and encourage themselves to a frequent attendance on that ordinance:
but if they find no present benefit, more exactly to review their preparation to, and carriage at, the sacrament; in both which, if they can approve themselves to God and their own consciences, they are to wait for the fruit of it in due time: but, if they see they have failed in either, they are to be humbled, and to attend upon it afterwards with more care and diligence.
It hit me that all the means of grace are this way: there may or may not be a blessing at the actual administration of the means, and the lack of blessing at the time of the means isn't necessarily because we sinned in preparing or somehow disqualified ourselves from blessing. In my own case for the Communion Season, the week leading up and the Lord's Day itself were filled with blessings from the Lord which should accompany this sacrament. Though not right at the Table, the blessings of Christ truly did come in a sensible way. And Christ was proclaimed that day by all of us present who partook.
So when you come to the Lord's Day and the children are a distraction, and as far as your duties allow you, you can say that you have prepared and observed and fellowshipped, be confident of a blessing. It may not be now, but it will come. Sometimes the Lord makes us wait for fruit, but it does come.
And if you haven't prepared, we must simply be humble ourselves, repent, and go again at the next opportunity.