I wish I had some advice for you but my 5 year old and 3 year old have never been on a plane. Good luck though. How long is the flight? Let us know how it goes.
When we flew to the UK 5 years ago my son was 2 my eldest was 5 and I was 32 weeks pregnant with the youngest,my pediatrician advised us off the record to give a small dose of benadryl so they would sleep better on the overnight flight.If you can afford seats get them both seats and take child car seats,we flew with Katie when she was 13 months old and didn't buy seats,at the end of 9 hours my arms were tired and my shoulder covered in drool!!
We just flew with a 21 month old and 7 month old to Australia... We bought our older son a seat b/c I wasn't going to hold both kids for so many hours... Instead of bringing the toddler car seat with us (borrowed one in Australia) we bought these simple straps that you add to the seat belt of the airplane that become like the straps of a car seat and your child cannot get out of the seat :). You can see it here: http://www.kidsflysafe.com/
If you didn't buy a seat for your 7 month old make sure to call the airlines right before you fly and see if the flight is full - that way you'll know whether to bother bringing the infant car seat to the gate with you.
One key thing is to use Huggies Overnight Diapers the whole trip because it's harder to change their diapers as often and you don't want to have any accidents... these will save you!
Also make sure that you put your stroller in a bag when you check it at the gate to protect it. I've heard of so many people lately that get to their destination with a damaged stroller.
Good Luck!
This is not an 'expert' opinion but rather a personal one:
Bring a DVD player for your toddler with many DVDs. When she is at her grumpiest put it on (with headphones and snacks) and she will be happy. The infant is more difficult. I always try to fly during nap time. This only works if he will sleep on you (unless he has his own seat). Remember to bring a bottle or cup to drink from during take-off and landing. You may want to give your daughter lollypops. This will protect their ears.
Good luck!
