I think that you were absolutley right in the first place thinking that Puerto Pollensa would be the right place for your family.
Please don't listen to the person who recommended the Bellevue in Alcudia to you- you will hate it and is totally unsuitable for the kind of person who goes to Pollensa. Its not that The Bellevue is awful perse, it's just that it's a huge complex with lots of Butlins type things going on- and in August which is the busiest time of year you can be sure that it is definitley not for you if you are not looking for a "piss up type place"- Sorry if this offends anyone, but it's sadly the truth. As soon as the school holidays start, you can be sure that as well as responsible parents, the Bellevue will have more than it's fair share of irresponsible parents who all get drunk on their duty free leaving their kids to run wild!
Alcudia might be ok, and is a good all-round choice, but best to book a package if you're going up there as it's quite a bit (90 minutes approx) drive from the airport so if you're having to pay for private taxi transfers it will be costly- The tour ops will charge anything from free to £18pp in the coach return to transfer you up there.
Alcudia is nice, again mainly for families and the accomodation there is excellent.
Try any of the "Viva" complexes for self catering, I liked the "Viva Blue" aparthotel, it's in a quieter area of Alcudia called Playa de Muro but it was excellent with great facilities- I'd probably go there again myself and can recommend it.
Most of the hotels there are ok too- avoid the All Inclusive Jupiter/Saturno if you don't like the crowds or Butlins abroad types of holiday. The 4 star Alcudia Mar is lovely- it's on an island setting at the marina, The 3 star Delfin Azul has (I think) just been refurbished and is airconditioned so worth considering.
Also be aware that there are essentially two parts to Alcudia- the coastal resort itself which runs around the bay and the more inland part up near the lake- picturesque enough but the mozzies will eat you alive so if you're going there, good insect repellent is an absolute must as well as a couple of plug ins for your room/apt.
However, I still think that you were right to think of Pollensa- it's a really lovely resort and appeals not only to mature couples, but very much so to families who are looking for something a little more "up-market" and appreciate it's beautiful location.
Puerto Pollensa is in the north of the island, not too far from Alcudia. Compared to the other beach resorts it has a lovely relaxed atmosphere in pretty surroundings. The beach is good, not too crowded and if I were going myself, thats probably where I'd stay and if I'm honest, the other resorts just pale into insignificance in comparison. Its definatley not for those looking for clubs and hectic nightlife but if it's restuarants, nice bars/cafes and you're the more discerning type looking for something that little bit classier, then Pollensa can't be beaten!
Check out The Duva apts, The Daina are excellent too and in a great location, The Habitat, The Hobby Club, Club Del Sol and the Villa Concha are also all OK.
For a hotel in Pollensa, The Club Pollentia is of the best as is The Daina Hotel and The Miramar- all are excellent- avoid the Pollensa Park if possible, it's ok though if you want busy busy and crammed with kids in high season and somehow it seems out of place in Pollensa.
One word of caution. Not all the hotels and apts in Pollensa have balconies in every room/apt, if this is essential, please check it out before you book otherwise you might not get one.
As for tips for saving money, you may be cheaper booking low cost flights with the likes of Easyjet and booking the accomodation seperatley yourself with a hire car or taxi transfer- this will especially be the case if you opt for self catering because you will be paying for the unit of accomodation in spite of how many occupy it (subject to maximum occupancy of course) This means you don't pay any underoccupancy supplelements that you certainly will pay for if you do opt for the traditional package through the major tour operators.
You may also like to know that online discounts are better than travel agents discounts on the high street so shop around online for the best deal.
If you fancy having a go at doing your own package with low cost flights check out the following for accomodation...
www.thomsonholidays.co.uk (they will sell you accom only very reasonably and they have a lot in Pollensa)
Finally, always check what you're booking on sites like trip advisor and holidays uncovered and read the reviews from other travellers before you part with any money- Look before you book :-)
I hope this helps you, but whatever you decide, I hope you have a lovely holiday!
Me! Been to Majorca over 20 times.