Our first trip to Benidorm was when our son was 9 months, we loved it so much we`ve been back 10 times in 7 years. All the bars and restraunts will make you welcome, remember the Sapinish love children. There are lots of coin opperated little rides for your baby. Poniente is our favorite side to Benidorm, at the end close to the old town is dove park your baby will be fasinated with the doves. There is a mini train going from behind here as well.
Mundamar is a nice day out.There are lots of lovely walks along the promanades which should keep you busy. If you go through the old town towards Levante there are a few street entertainers, Silver man, Gold man and a clown, our son loved to see these but was petrified of the clown. Tapas alley is a nice place for a drink and nibble, lots of Spainish take all the family along to here.
If you head toward the end of Levente (might be best to get a taxi) there is a bar called the Celler bar, each night Louis the clown does his show.
I`m sure if you ask in the hotels they will let you use pool.
We have had some fantastic family holidays in Benidorm.I`m sure you will also.
Christine