I also suggest simply walking through old town marbella and you will surely find restaurants that are holding new years eve parties. There is always a festive atmosphere and people walking through the streets there so you will be in the middle of it all if you stick to this area. At midnight the town hall rings in the new year with a big party on Plaza de la Iglesia in Old Town with a chance to take part in the 12 lucky grapes tradition. There is a party also held in San Pedro at the Plaza de la Iglesia there if this is closer for you. The crowds may be a bit smaller, which is maybe an advantage as you are with your 7 year old.
I also hear that the restaurant Nuevo Reino in San Pedro on the beach is having a great party. I have friends who are going there and they have lots of kids, so you will surely find children running around there.