This is a situation where you need to be flexible and able to play it by ear. Evaluate which child is the highest risk for lasting the shortest amount of time before they become harder or impossible to work with. Balance that with any child that is already being difficult and might do better if you save them until later when they might be more manageable. Unless you already know each of the individuals involved, you'll need to wait until they arrive for the session to do your initial evaluation.

You should take the photos involving those most likely to "fade" or become "too agitated" the longer they are there first and then work from there. At the same time, save those who already appear to be more than a handful until later.

In general, I'd work with the individual portraits of the 10 and 15 month old babies first, then do the groups shots, and then finish with the two older children who should have more staying power. But if the 5 year old comes showing evidence "someone" missed their nap today and the babies seem content and manageable I might do the 5 year old and then the group shots first to try and get something usable before the dam breaks.

On the other hand, if one of the children enters like a tornado and is already at the point of being very difficult, save them for last. Maybe they're not so sure about the unfamiliar person with the camera and seeing their siblings survive being photographed by you unscathed will settle their fears. Or maybe one of the parents will be able to soothe a fussy baby while you're doing the individual portraits of the older kids.