not much unless you intend doing trips etc which I don't think you will be with the little ones - if your all inclusive is good and covers all the meals and drinks you want and you don't intend going out much then whatever you will need for essentials for the baby (nappies/bottled water etc) plus something for treats and emergencies - I'd have thought maybe about 50 euros a day? how much would you normally spend on a day out here with no meals to buy?
I don't know the place but as a rough guide, it's only a week, bank on a few day trips at what ? Say £40 per person ? Take enough for a few drinks each night and a few ice creams and soft drinks in the day. A few souvenirs too. and the odd taxi ride maybe.
Take what you can afford and budget to that. Take more and you'll spend more. Take your bank/credit card in case of emergency.
Yes really depends on what you want to do like excursions etc. If you wanted to do a show in the evening like the Pirate show in Magaluf then that will cost around 150 euros for the family or a trip on the Soller railway can cost anything from 150 euros if you go on an excursion with company or maybe 40 euros if you catch the bus to Palma then the train on to Soller and Puerto de Soller which isn't too difficult to do. Buses are not expensive and regular or there are a few places near by which can be reached by taxi.
If you bank with someone like Nationwide it's a notional charge only per transaction, they charge £1 and a small amount of commission (2%) - but it's so much safer that taking large amounts of cash with you. We wouldn't do it any other way.
We've started taking some cash and this year taking some on one of those cash cards which can be used as a debit card or to take out cash from hole in wall. Will be cheaper using one of them rather than using money from our bank as they charge too much. Some banks charge more than others and ours is one that likes to charge.