This is a general summary of what seems to be this forum's positions on the participation of children in weddings:
1) The children in question can participate in the capacities of guest, MOH, BM, bridesmaid/man, groomsman/maid, reader, usher, flower girl, or ring bearer, depending on their ages. Kids ages 3 to 7 can be flower girls and ring bearers; kids older than that can participate in the other capacities.
2) The children in question need to be able to understand and remember even in a limited way what they are being asked to do. For this reason, it is not advised that children under age 3 participate in any capacity other than guest.
3) The children in question need to be able to get up and down the aisle on their own or in wheelchairs or with crutches or canes. Wagons and carts should not be employed for the purpose of "including" children under the age of 3.
4) Children of all ages can participate in photo shoots.
5) The wedding ceremony is not the place to give "family unity" gifts to children. This should be done in private.
6) Children should not be expected to say vows to new stepparents during the wedding ceremony; nor should new stepparents recite vows to stepchildren during the wedding ceremony. If this is done at all, this should be done in private.
7) The participation of children should always be cleared with the other parent if they are in the child's life. That one parent is remarrying does not automatically have the new stepparent replace the other parent as the child's other parent if that is the case.
8) The marriage of a parent often evokes strong emotional responses from children which are not always in the parent's and/or new stepparent's favor. Also, some children are just shy or would otherwise feel uncomfortable participating. Any desire on a child's part not to participate in a wedding for whatever reason should be respected-it should never be forced or sprung unexpectedly on a child.
9) No religious or cultural tradition that does not exist explicitly for the purpose of the participation of a child or stepchild should be altered for use as a "unity ceremony." This is not respectful to the religion or culture that is the source of that tradition.
10) While anyone can do whatever they wish at their own wedding, these positions are based on the idea that the wedding is the union of the couple, and children play a peripheral (still important, but not top-billing) role and are not the stars of the show, and are not meant to offend anyone but to set forth guidelines on how children of any age can best participate with the least likelihood of offending anyone and/or causing side-eyes.
Obviously, individual members might differ with one or more of these principles; this just happens to be a summary of what seems to be the most commonly held positions.