Here is an excellent article by Jeremy Walker on the matter of children in church:
ATTENDANCE OF CHILDREN IN PUBLIC WORSHIP SERVICES.
The church is not exempt from responsibility: we should declare with David the fear of the Lord to the children of the church, and seek to manifest the same tender regard for them, and insight into their upbringing, as Christ and his apostles
by JEREMY WALKER
"Come, you children, listen to me; I will teach you the fear of the Lord." (Ps 34.11) "From childhood you have known the Holy Scriptures, which are able to make you wise for salvation through faith which is in Christ Jesus." (2 Tim 3.15).
The constant presumption of Scripture is that children were present in the worship of the people of God. In Nehemiah’s time, men and women and all those who could hear with understanding gathered to hear Ezra the scribe read the Law (Neh 8.1-3; Ezr 10.1). Moses certainly anticipated the literal ‘children’ of Israel to be present when the Law was read (Dt 31.12-13). Paul’s letters, intended to be read to the churches, assume the intelligent presence of children (Eph 6.1-4; Col 3.20), and children were present when the Lord Jesus taught (Mt 18.1-5; 19.13-15).
Observe that this is an intelligent presence. It is neither a merely formal nor a distracted attendance. Moses’ desire was that ‘the children may hear . . . and learn to fear the Lord your God and carefully observe all the words of this law’ (Dt 31.12). In Neh 8.1-3 ff., there is active participation and response in hearing the reading and explanation of the book of the Law. The children present are intelligently involved in what is going on. Moses wanted parents to be ready to answer knowledgeable questions from their children arising from the worship (Dt 6.20-25); Joshua wanted Israel to take advantage of the natural inquisitiveness of children (Jos 4.5-7).
All of this, of course, is in the context of parental instruction, and a prayerful concern for the good of a child’s soul (Dt 6.6-7). Children can and should remember their Creator in the days of their youth (Ecc 12.10). Hannah’s care for Samuel (1Sam 1-3), the godly atmosphere of young Timothy’s home (1Tim 1.5), and the parental concern of Solomon (e.g. Prv 2.1-9) all provide models and encouragement. Examples from Scripture and church history illustrate the possibility of the very young being granted saving faith in Jesus Christ. The church is not exempt from responsibility: we should declare with David the fear of the Lord to the children of the church, and seek to manifest the same tender regard for them, and insight into their upbringing, as Christ and his apostles (Mt 18.1-6; 19.13-15; Eph 6.1-3; 1Thes 2.11). All the members of the church should help to establish an atmosphere in which parents can raise children in the training and admonition of the Lord (Eph 6.4).
With a view to a more careful adherence to the Biblical model, we therefore suggest that children of at least school age (although there need be no arbitrary distinction — some younger children might be well able to be present at an earlier age) should be present in the public meetings of the church (especially the morning and evening services on the Lord’s day). We would also suggest that parents consider bringing children to mid-week meetings, particularly during the school holidays.
The children should sit quietly and attentively, endeavouring — to the best of their ability — to participate reverently and intelligently in the various exercises of worship. To attain such a goal requires that parents be diligent and thorough in preparing their children for attendance at and participation in the public meetings. In order to help parents, and the church, accomplish their Biblical responsibility, we have prepared the following guidelines, which we hope will act as an aid to such preparation.
1] Conduct family worship daily. Incorporate elements of the public meetings into the fabric of family worship where appropriate, demonstrating an active regard for and interest in what has occurred in the public meetings, and showing that the content of those meetings is relevant beyond Sunday. For example, consider singing hymns recently used, or read from the same passages of Scripture, or take up matters for prayer from the prayer meeting. Where necessary, practice the behaviour required in the worship services. Consider the particular relevance of family worship on Saturday evenings, as a means of preparation for the Lord’s day. Use the opportunity not only to prepare the heart for worship, but also to remind your children of the behaviour expected of them on the Sunday.
2] Seek to order things in your home so that children have adequate rest on Saturday night (we ought to be at least as concerned that children get enough as sleep as on a school night), and have adequate time on Sunday morning to prepare to leave the house, so that they are in every respect ready for church.
3] Aim to arrive in good time (perhaps 10-15 minutes before the service begins), and be in the appropriate place for worship as soon as reasonably possible. Remind children in advance what behaviour is expected in Sunday School, the worship services, and/or the prayer meeting.
4] Accomplish necessary tasks (such as getting a drink, or using the toilet) before the beginning of the service.
5] Assume that your child will sit through the entire service unless there is a particular reason for leaving. There is no need to leave the worship at the first sign of disturbance from your children: churches should appreciate that children are children, and that there will be times when they do not behave perfectly. If there is no alternative, take your child out of the service. Ensure that this is not seen as a ‘reward’ for disobedience, and, if possible, deal with the particular issue appropriately and immediately, and then return to the meeting room to continue participating in the public worship of God.
6] Train your sons and daughters to be good listeners, sitting with good posture and focusing their eyes on the one leading the service or preaching. When the Scriptures are read, have them turn to the text and follow in their own or your Bible. Likewise, help them turn to each hymn and follow from the hymnbook, helping them as required. With older children, consider means (such as taking notes) of helping them to concentrate.
7] Remember that leaving a public meeting (even for legitimate reasons) is a distraction, at least to those nearby, and that such a departure interrupts your worship of God. It will impair your ability to follow, understand, and therefore benefit from the preaching of God’s word. The logic and continuity of Biblical preaching is lost when there are gaps and interruptions in the hearing of it. Seriously consider the possibility that your child’s desire to leave the meeting place be refused.
8] If it is predictable that you will need to take your child out of a service to train or discipline him or her, aim to take seats near the doors of the meeting room, where you can get in and out with least distraction to others. When leaving or entering, try to do so with a minimum of fuss and noise. Other members of the church — deacons or door stewards, for example — might be able to help ensure that such seats are available. If you have an appropriate seat, you can retake your seat with minimal distraction when you bring the child back in to the service. Remember that the children are to participate intelligently in worship — diversionary activities (drawing, writing, playing, etc.) are not a part of the worship of God. Neither (outside of the Lord’s supper) are eating and drinking, which can be distracting for the child, yourself, and others.
These things will undermine a child’s active and intelligent involvement in the worship of God
9] Encourage children to continue behaving well (e.g. not making excessive noise and shouting) inside and outside the building, after a public meeting. Help children to behave politely to one another, and to adults (holding open doors, helping with tasks, etc.), and to behave in a friendly fashion to visitors, particularly visiting children.
10] Where possible, follow up the preaching and teaching with your children (during the drive home, during lunch, in family worship on Sunday afternoon/evening), asking them questions appropriate to their level of understanding.
11] Remember the power, for good or evil, of your own example in preparing for and participating in the public meetings of the church.