I don't know the minds of those proposing the change. Is this the "I don't think it is wrong to throw a ball with my son" kind of recreation or something more than that? I think there is a fundamental ignorance of the actual puritan view and not just a misunderstanding of one term. I'm not saying that the fears of just how restrictive it is will not prove true; but it sure seems like there is at least some level of misunderstand judging from just the questions I have received from people and I have zero standing on the matter. If this is about a certain level of latitude for a 'child's sabbath' or doing some activity with an energetic child that needs his spring sprung, I think that can be discussed within the scope, limits and exceptions of the Puritan understanding of the fourth commandment. But, given what the actual practice is in the PCA, I don't think this is about that kind of thing. I could be wrong. From one prof's question to me about this I wrote the following. I open to the board's puritan experts correcting or refining any of it.
I toss this out as a summary of my gleanings from various ‘approved’ authors. I don’t think my take away is too strict; my fear if anything is that it may be too loose or permissive. It also does not exhaust the subject but I hope it gets if briefly and perhaps clumsily to general principles. If this question merely bewilders, then a study of the broader question of a Christian Sabbath is in order but that is assumed here.
What are the Westminster Confession of Faith and Catechisms getting at when they prohibited as a breach of the fourth commandment the engaging in our otherwise lawful pastimes and recreations on the Lord’s Day? The confession reads at chapter 21, §7-8,
VII. As it is of the law of nature, that, in general, a due proportion of time be set apart for the worship of God; so, in his Word, by a positive, moral, and perpetual commandment, binding all men in all ages, he hath particularly appointed one day in seven for a Sabbath, to be kept holy unto him: which, from the beginning of the world to the resurrection of Christ, was the last day of the week; and, from the resurrection of Christ, was changed into the first day of the week, which in Scripture is called the Lord's Day, and is to be continued to the end of the world as the Christian Sabbath.
VIII. This Sabbath is to be kept holy unto the Lord when men, after a due preparing of their hearts, and ordering of their common affairs beforehand, do not only observe an holy rest all the day from their own works, words, and thoughts about their worldly employments and recreations; but also are taken up the whole time in the public and private exercises of his worship, and in the duties of necessity and mercy.
And the Westminster Larger Question asks and answers in Q&A117.
How is the sabbath or the Lord’s day to be sanctified? (see Scripture proof texts in versions of the Westminster Standards; omitted here for brevity).
A. The sabbath or Lord’s day is to be sanctified by an holy resting all the day, not only from such works as are at all times sinful, but even from such worldly employments and recreations as are on other days lawful; and making it our delight to spend the whole time (except so much of it as is to be taken up in works of necessity and mercy) in the public and private exercises of God’s worship: and, to that end, we are to prepare our hearts, and with such foresight, diligence, and moderation, to dispose and seasonably dispatch our worldly business, that we may be the more free and fit for the duties of that day.
Organized, time consuming, sports, amusements, pastimes (think time spent watching the game), etc. are indeed prohibited on the Lord’s day by the fourth commandment (concluded from the prohibition of the greater, laboring, reasoning to the lesser, our pastimes and recreations). But there is not in this view a total prohibition of activity, any more than there is of eating or sleeping. We need appropriate amounts of these to function on any day and moderate use of all these is necessary to be alert and capable for observing the worship of the Lord’s Day. However, while an individual needs some level of all these, which will vary due to individuality and circumstances, perhaps medical necessity, this is no more a permission to run some miles, than to ‘pig out’ feasting, lounge away the Lord’s day in bed, etc.
In general, as with rest and food, we may require modest activity to keep us alert (or in children perhaps to blow off some pent up energy), but such bodily activity should be always directed within the confines of what is necessary to keep us fit and on track for the duties of the day. Can one take a walk on the Lord’s Day between worship services? Casually toss a ball with a child? Perhaps, perhaps not. Can it be done while turned to a good use of the time in keeping with the Lord’s Day? Are such things something you already do during the week and how does a proposed activity comport with putting aside our normal pastimes as we do our normal weekday labors to observe the Lord’s Day? Is it an incidental thing to blow off some energy or does it turn the heart away from the purpose of the day or end up simply burning time that could be spent in private and family acts of worship? Are we of a mind to keep a Sabbath of the mature, or of a child (cf. Rutherford’s Catechism, Catechisms of the Second Reformation, [1886] 232)?
The root question over modest bodily activity as opposed to recreational pursuits on the Lord's Day, is, will they comport and aid the duties of the day, or will they distract, consume time, and merely unfit us for observing the worship of God? Convenient food, rest and activity (perhaps in decreasing importance?) are necessary in their place, but should be subservient to the purpose in view of spending the day in the public and private worship of the Lord.
It strikes me that Gouge on the Family or Baxter's work may have something explicit on this but I am not familiar with either work.