1. Travel while they are still young. Traveling with babies who are breastfed is the easiest (food is always at hand). Airline tickets are free for children up to two years old. Except! Once on easyjet it happened to us that an infant ticket was more expensive than an adult (but probably because the adult tickets were ridiculously cheap - 5€).
2. With infants up to two years old, you can travel with two children's items: a car seat and a stroller, or we mountaineers took a Deuter/Osprey instead of a stroller. (Another tip: you can fill the pocket of your backpack, no one weighs it.) ).
3. Admission is cheaper or free for little ones. If your children look younger, take a year off, they usually don't require ID anywhere. 
4. Take some luggage. Usually the four of us travel with one suitcase (20kg) and hand luggage. Enough. I prefer to find accommodation with a washing machine and wash the dirty clothes so that we can wear them several times. (Always check if the accommodation also includes sheets and towels).
5. A child's plane ticket includes a free car seat. We always take our own seats and save money because renting a car seat usually costs around €40. We wrap them in foil to protect them from airport dirt. 
6. Airfares to places around Europe are ridiculously low and have been at the lowest cost lately.
7. Don't complicate your diet. No one has ever died from eating only pasta, pizza, soup from a bag, salami, and pâté for a week.  Although I admit that I absolutely need AT LEAST one hot meal a day. 

The most difficult period for traveling with toddlers is once you introduce solid food, which is around two years old. A period when you can't tell them to sit down. Nor can you expect them to. I don't advocate tablets myself, so more entertainment is needed during this period. After the age of three, you simply distract them with books, drawing, coloring, toys. Unfortunately, my two don't nap on the plane.  But then there is this period when travel becomes both easier and more expensive.