We are going december and staying in los Cristianos for about the 7th time.
The beaches are lovely and the sea is much calmer around the harbour for them to paddle. It's a manmade beach but very nice, yellow sand and lots of it is wheel/pushchair friendly.
Look for a hotel with a heated pool though, it will be a bit chilly in the pools in feb for little ones.
There is a little park just near the harbour and another couple dotted around. There is a bar on the seafront called Balous I think it is. Bit of a trek up the steps but has a little play area at the back that ds (4) loved.
In the expat/residential area up the hill there is a shopping centre with a massive kids play are on the top. A soft play bit, some little rides/arcade games,a bar and a couple of places to eat.
Lots of the restaurants/bars are geared up for familes and come 11pm most things are closed so nice and quiet at night.
People are a bit sniffy about tenerife. We have been to greece a few times, all the balerics and mainland spain but always go back to Tenerife. Dd is 14 now, been going since she was 3 and she loves it.
We stayed in the HG Tenerife Sur last time and have just rebooked the same hotel. Its cheap and cheerful but suits us, the pool is nice, it's very clean and quiet and is central. Its cost us £900 for a week sc for a family of 4!
You can walk down to las americas and even down to costa adeje if you fancy the walk, its a lovely coast walk. We usually get a taxi back though as its a bit far to walk both ways.