6 months before you travel check carefully what immunisations your children have and what they need for each country and get those done at home before you travel. Personally we avoided any malarial areas as I didn't even want to have to think about putting a 1 and 4 year old on anti-malaria tablets.
Take everything that you need with you - cots are not readily available unless you are staying in high end hotels because in South and Central America they normally sleep with their kids in the same bed as them. We didn't take a travel cot with us and then realised our mistake and so had to buy one and get it shipped; it cost us a lot of money and time. Don't do this, there are plenty of really good and lightweight options available in the UK. We had to buy a travel cot in Galapagos for our stay there and it cost $200 for something that would have cost us around £50 in the UK. Pushchairs are very useful for carrying heavy stuff and daytime sleeping, etc. Bring a travel booster seat as highchairs are few and far between. If you want to hire a car then you will need to bring car seats as these are non-existent unless, maybe, you are hiring from an international dealer.
You need to wash all fruit and vegetables being consumed raw. You can buy fruit and vegetable disinfectant solutions in some of the countries or you can use bicarbonate soda mixed in tap water (one tbs per litre), which you can find in supermarkets and smaller shops often will have some too.
Start practicing your Spanish before you leave the UK - Duolingo is really good!
Download the Spanish language files for Google Translate before you leave the UK.
Take as many crafting/drawing/sticker books with you as you can as although you can buy some basic bits it is not as easy to find depending on where you are.
Have a good durable electronic device for the kids. Then they will have plenty of books to read, games to play and activities to keep them occupied. You can also use these for home-schooling. You need to take additional storage space to go with this if the internal storage is not very big.
Download lots of books, games and videos on a device for kids as the internet can be very sketchy in place and basically non-existent in Galapagos.
Country specific advice
Ecuador and the Galapagos Islands
Ecuador is expensive for South America and the Galapagos Islands are very expensive by any standard.
Nappies and wipes are really expensive so take as many as you can with you if going to the Galapagos Islands. We found that a pack of nappies was costing us between $40-$50 for a large packet.
If you are going to the Galapagos Islands then staying on Santa Cruz in Puerto Ayora works well as you see lots of wildlife there and there are many play parks and beaches for the kids, although some of the beaches are not easy to get to with young kids.
We went to Isabela Island on the boat. The boat was very rough at the time of year we were there so not good for the kids.
Isabela Island was good to stay on with the kids as the beach is by the town, so easy to access and it is quieter there. We found that there are less play parks, etc., but found a couple of good ones.
The internet in the Galapagos is really bad, so be well prepared by having everything you need downloaded before you go.
Colombia
If visiting the Santa Marta/Seirra Nevada area then bear in mind it is rough around the edges. Taganga is loud and although being near the front would be nice, it is too noisy for sleeping children. The area south of Santa Marta is probably a better bet for a quieter experience.
Places along the road from Santa Marta towards the Tayrona National Park are lovely and the area is beautiful. The park itself is tricky to see much of with young children as many areas are only accessible via 3 hour treks on slippery wet paths however it is still worth popping in. We stayed in Calabazo which worked out well for us.
Palomino is a much quieter beach area than Taganga, but the sea is far too rough for anyone! If staying in Palomino then I recommend a nice hotel near one of the many rivers that you can swim in. This would be better than being near the sea for little ones and having a pool is very convienent.
Cartagena is lovely and a good area to stay with kids is El Laguito. It is pretty quiet apart from the occasional party bus driving past and most places have swimming pools as well as you having many beach options close by. There are also lots of supermarkets, shops, cafes and restaurants in the area which is very handy with kids.