As one of your top requirements seems to be a Hilton, an option I suggest would be
Hilton Sa Torre Mallorca hotelin Majorca.
Tripadvisor doesn't do it bad ..... Great for kids with pools etc.
Majorca is a family holiday destination that is regenerating into a reasonably sophisticated destination - and in particular Palma which is not to far from Llucmayor which is wherre this Hilton is located.
Palma should be a cheap flight from Madrid and I think would be ideal for a family stay for a few nights. Much better than Madrid in my view although I'd feel a lot happier if someone else posted enthusiastically in favour of Madrid to give a counter opinion to my own. Hate to give you a bum steer.
If you want any more pointers with respect to Majorca just ask.