If you look online, per the Airline's website, they will often have the rules or policies of children traveling unattended and what to do etc.
And, I would also recommend, having some kind of "consent to travel minor without parent" or "Consent to travel for minor aged children" type form. So that they can also carry it on them, (you retaining a copy of this form for your own records). Look online for these forms. It is typically free, and they have templates for you to use.
I have done that. Or a "consent to travel minor with one parent" type form.
These types of forms, sometimes have to be, Notarized.
And to have, copies of their medical/insurance info. and some kind of I.D.
And, take CURRENT photos of your children, BEFORE they go on that trip, so that if they are lost or anything, you have CURRENT photos of them to show officials. And info on their current height and weight etc. per descriptions of them.
And mostly, there should be formal legal documentation/custody orders, that they CAN go, out of state and travel and do that.
Everything needs to be legally processed and determined.
And make sure, they have ROUND trip, tickets purchased.... and, a time frame, in which you KNOW the kids will be returning.
AND a contact number for your Ex, AND his CURRENT address of his residence... and/or of his current Employer and their phone number too. Should you have to contact him and cannot and you then need to contact his office or Employer or anything, just in case or just in case you cannot make contact with your Ex or if he does not answer his phone or cell phone. And if he will not give you this information freely, then I would not trust, him.
AND have or get a cheap cell phone for your 10 year old, to use, ANYTIME. Teach him/her how to use it. And how to call you no matter what time it is. AND that, his/her Dad cannot take it away from him/her.
A 10 year old, flying with a 5 year old, is daunting.
They are not a "babysitter" and may NOT even know... how to manage their younger sibling, much less on a flight.
I would not consider this.
And there are probably age limits? Per how old a kid is in order to fly by themselves????
LOOK into that.
And lastly, you do not HAVE to, allow this. Unless your and your Ex's custody "rules" are allowing it.
If you do not even have, any child custody papers per the courts nor anything legally formal about your "separation" and do not have ANYTHING, per custody or who has rights, I would not do this.
I have an 11 year old and a 7 year old.
I would not let them fly alone... even if my 11 year old is very mature. I would not have her be a "parent" to my 7 year old much less "manage" him on that entire trip. Even if they are good normal kids. Even for a parent, managing a young kid on a flight can be daunting.