I've been to Tenerife many times - at various times of year.
The sea is often chilly as it is the Atlantic. However once you are in, it's fine
Most hotels have heated pools.
April should be warm. I have been in mid April - it was glorious weather.
There is loads to do in Tenerife.
Mount Teide is a must. You can hire a car and drive up, or take a bus trip. If yourDC are happy to sit for a few hours, it is very educational on the coach. Younger children might be free/cheap. We have done it both self-drive and coach. The cable car to the top of Teide is fab- a bit pricey perhaps for all the family but really worth it. Get there early as the queues can be long (and take a jumper, it's cold up there!).
I have stayed at Sheraton La Caleta - went for our honey moon actually. Nice hotel. There isn't too much to do in the immediate area, but a short walk to the small beach and then further on to Del Duque area, with beach.
If you like seafood then turn right out of the hotel and walk up to La Caleta itself. Some great fresh seafood - one right on the point, with outdoor plastic tables and chairs is fab. Can't get a better view - or chipirones!
Restaurants in Playa Del Duque area are a bit expensive - and there aren't many, but things may have changed since I was there.