You can claim Child Tax Credit for a child or a young person who normally lives with you. A child or a young person can only be included in one household at any one time. If you have shared responsibility for a child and are unsure who should claim then please contact the helpdesk on 0845 300 3900
However, when residence is on a fairly even basis, and parents are in agreement and talking (like you and your ex), some do agree that the lower wage earner claims CB and CTC for all children concerned as this benefits the children.
Depending on how close you live to each other, you might want to review the situation when the elder child gets nearer secondary school age. Whether a child lives in a school catchment area is determined by who gets the child benefit. So it is worth your while making sure that the parent who lives nearest to the secondary school you want your younger two to go to gets the benefit for the six year old to increase their chances of getting in. Then the younger one (for whom the other parent claims child benefit) can follow them on the basis of the sibling rule.
There is no hard and fast rule. The benefits system is not really equipped to deal with shared residence arrangments.
it is possible for the tax credit to be paid to one parent and the CB to the other, the only probnlem would be is you both tried to claim the same child.
It may well be strictly fair for you to cliam (that way, each of you claims for one of the two childnre for whom you share care, and you claim for the child who lives with you full time, however, It sounds as though you have done really well to reach an amicable agreement with your ex which benefits all of the children, and it would be a shame if that came to grief over the benefits.
Why not try to come to an agreement that the money is claimed by (say) you but that you agree to pay a share of it to your ex? Even if this is only a relatively small amount it shows good will and may help you to get along better, which is likely to be in the children's best interests.
Once the 16 y.o leaves education and you can no longer claim CB or TC for her then it would be appropriate to review the situation and for you each to retain the benifits for one child.