Granted, I'm from the US and different rules may apply here.
But I think you are okay with inviting the children of relatives and not the children of friends. The children you are related to and who are traveling--there really isn't anyone to take care of them, as all the rest of the family will be at the reception.
If your friends question this, just tell them the truth. You invited the children of close family members to the reception, but did not have room for the children of friends. Most people will understand prioritizing family over friends*.
As for how to make this clear when inviting people, the simplest way would be to have separate invitations for the events. One for the wedding and the meal directly following it, on which you carefully list the exact names of the people you are inviting--parents and children. Then for the reception that follows on a different day, a separate invitation, with just the names of the parents.
Will you be doing RSPVs? If anyone responds that they will be bringing uninvited guests to the reception, you can gently inform them that while the parents are welcome, space simply does not allow for their children.
*Although I did once attend a cousin's wedding where her 10 year old brother was present, because, you know, it was his sister's wedding. A wedding guest, who apparently had asked if her children could attend and was told no, they could not, threw a temper tantrum in the middle of the reception, yelling that if one kid was allowed, then her kids should be allowed. It was pretty weird.