Hi we went to the galea last week, and there are loads of car hire places within a 5 min walk, the nearest being 100 yards from front door next to tachice hotel.
Nigel I would say the hotel and resort are fine for children, although we went as a couple. There appeared to be some entertainers around, and costa teguise feels a safe area for kids. The hotel is 5 mins away from both beaches via front door. and back door leads out on to promenade at the front.
There is a water park at back of costa teguise, going out towards the golf course, and this might be good entertainment for your kids age group.
The only thing I didn't see was entertainment for kids in evening, there might have been some and I just didn't notice it i.e. to busy at the cocktail bar round corner. If that is the case and the kids get bored the tachice next door seemed to caberet every night, you could nip in there with them, and have a few drinks.
Cheers Bellana.