Honestly sounds a lot like simply moving the modern religious enterprise into somebody's living room.
Forget house church vs "institutional" church for a moment. Think instead
Biblical church. Instead of taking the liturgy and structure of the denominational world and trying to squeeze it into a "small group setting", why not take the Bible as the blueprint and just do what they did the way they did it?
Who decides who is going to teach? How about God?
Romans 12:3-8 KJV
For I say, through the grace given unto me, to every man that is among you, not to think of himself more highly than he ought to think; but to think soberly, according as God hath dealt to every man the measure of faith. [4] For as we have many members in one body, and all members have not the same office: [5] So we, being many, are one body in Christ, and every one members one of another. [6] Having then gifts differing according to the grace that is given to us, whether prophecy, let us prophesy according to the proportion of faith; [7] Or ministry, let us wait on our ministering: or he that teacheth, on teaching; [8] Or he that exhorteth, on exhortation: he that giveth, let him do it with simplicity; he that ruleth, with diligence; he that sheweth mercy, with cheerfulness.
1 Corinthians 12:4-12 KJV
Now there are diversities of gifts, but the same Spirit. [5] And there are differences of administrations, but the same Lord. [6] And there are diversities of operations, but it is the same God which worketh all in all. [7] But the manifestation of the Spirit is given to every man to profit withal. [8] For to one is given by the Spirit the word of wisdom; to another the word of knowledge by the same Spirit; [9] To another faith by the same Spirit; to another the gifts of healing by the same Spirit; [10] To another the working of miracles; to another prophecy; to another discerning of spirits; to another divers kinds of tongues; to another the interpretation of tongues: [11] But all these worketh that one and the selfsame Spirit, dividing to every man severally as he will. [12] For as the body is one, and hath many members, and all the members of that one body, being many, are one body: so also is Christ.
1 Corinthians 12:18 KJV
But now hath God set the members every one of them in the body, as it hath pleased him.
1 Corinthians 14:26-33 KJV
How is it then, brethren? when ye come together, every one of you hath a psalm, hath a doctrine, hath a tongue, hath a revelation, hath an interpretation. Let all things be done unto edifying. [27] If any man speak in an unknown tongue, let it be by two, or at the most by three, and that by course; and let one interpret. [28] But if there be no interpreter, let him keep silence in the church; and let him speak to himself, and to God. [29] Let the prophets speak two or three, and let the other judge. [30] If any thing be revealed to another that sitteth by, let the first hold his peace. [31] For ye may all prophesy one by one, that all may learn, and all may be comforted. [32] And the spirits of the prophets are subject to the prophets. [33] For God is not the author of confusion, but of peace, as in all churches of the saints.
Notice the part that says "If anything be revealed to another that sitteth by, let the first hold his peace. For ye may all prophesy one by one, that all may learn, and all may be comforted."
Those are some of elder Paul's instructions for the meeting. Surely we will submit to the instructions of a bona fide apostle of the Lord?
Here are some other instructions:
2 Timothy 2:2 KJV
And the things that thou hast heard of me among many witnesses, the same commit thou to faithful men, who shall be able to teach others also.
1 Timothy 5:17 KJV
Let the elders that rule well be counted worthy of double honour, especially they who labour in the word and doctrine.
Elders are responsible for The Teaching, but they are not the only ones who are to teach. The job of an elder and bishop (episkopos, overseer) is to "look upon" or "oversee" what goes on in the group, and correct by the Word any errors. This is why Paul taught us:
1 Corinthians 14:29 KJV
Let the prophets speak two or three, and let the other judge.
What is taught, whether by doctrinal presentation or alleged divine utterances, are to be judged. Judged as to the message's conformity to the Word of God, its expediency, and application, to the assembly, etc.
The Bible contains the "structure... and appointment..." for the assembly to do its thing. And we need to really get away from viewing church as a "group that meets on ___day". Church is more than a meeting or "service". It is a COMMUNITY, literally an alternative society (alternative to the world). It is not just a "part" of our lives, it IS our life, it is 2 or more people living for Jesus - together.
This is why we see this:
Acts 5:42 KJV
And daily in the temple, and
in every house, they ceased not to teach and preach Jesus Christ.
Acts 20:20 KJV
And how I kept back nothing that was profitable unto you , but have shewed you, and have taught you publicly,
and from house to house,
It's not just group meetings. It is constant interactions and teaching and ministering, especially outside of the main gathering.
As for children, they are simply adults-in-training. They do best with the best results by simply being with their parents in the meeting, learning by example how to be functioning Christians. It's great that you encourage them to participate, and every meeting needs to take into account every member, and minister to each regardless of what "level" they are at. But care must be taken to avoid giving ANYONE, whether a child, an adult, a visitor, or a preacher, the idea that the meeting of God's church is to be somehow altered for them and their personal wants. Otherwise, church becomes entertainment, regardless how "serious and somber" things may appear.