I can only comment on the BA Avios scheme so hopefully I can shed some light on it.
First of all you have to be a member of the BA Executive Club to book avios flights with them, its free to join & you can sign the whole family up & create a house hold account which means that you pool your miles / avios, you can also transfer your miles direct to your Exec Club account from your avios account.
As other people have said, booking any kind of reward flight with BA during school holiday or other popular holiday times is difficult & requires a fair degree of planning & persistence but it can be done.
What BA or any other airline for that matter do not do is offer unlimited reward flights, if they did they would soon be out of business.
If I am being honest you have probably left it too late to book economy reward seats for July next year but keep looking & you may be lucky.
BA tend to release reward seats one year in advance & then drip feed more into the system depending on passenger load, time of year & other factors, they also release reward seats closer to the flight date.
From what I know, there is no hard & fast rule as how many seats they release per flight but anecdotally the figure of two seats per flight per class keeps getting mentioned. N.B. Do not quote me on this as I may be wrong.
By far the best use of Avios miles is to use them to upgrade to the next cabin i.e. World Traveller to World Traveller+, World Traveller+ to Club World or CW to First.
You can if you are quick grab reward seats when they are released but you will probably find yourself with the same dilemma that we did when we booked for Florida last November.
We had collected enough miles, via BA domestic flights, a few business class flights with Aer Lingus, Tesco Club Card points & our American Express cards to go for the WT+ to CW upgrade option which means you pay for WT+ & if available you upgrade to CW for 25,000 miles each.
One year out & I had two flights ready to book but then the stinger, the return flights had not been loaded yet, of course two weeks later when they were added, the outbound flights had gone.
I kept an eye on the flights on & off for the next couple of months & then in mid-January they came up & I booked them there & then, the old adage of you snooze you lose is very, very true when it comes to booking BA flights with avios.
Another trick with getting flights is to be flexible when & where you fly to, we ended up flying to Miami which worked for us as we had a few days in South Beach before driving up to Orlando, there is no better feeling than paying for WT+ & then flying out & back in CW & trust me once you have reclined that seat into bed mode you will not want to fly across the atlantic down the back of the plane again.
You can also use BA avios on partner airlines, i.e. American & Aer Lingus.
Weve only flown business class with Aer Lingus so cant comment on what their economy service is like but pre clearing US immigration & customs in Dublin is brilliant & the immigration guys are also way nicer, you land in the States as if its a domestic flight so dont rule them out as I am sure they charge less in avios & taxes, you have to call the BA Exec club who can check on availability for you.
My advice would be to keep collecting avios & they will soon mount up, if you are short of avios for a trip you can buy them from BA which we did once when we were novices at collecting them, there is a deal on at the moment which offers you a bonus depending on how many you buy, BA also offer miles plus money as an option
I have seen quite a few people on hear complaining about the charges that you have to pay when booking avios flights, the charges do not go to the airline, they are the taxes & security charges that you would pay anyway if you were paying cash for your flight.
I have to admit that I used to do a lot of flying with BA when in a previous job & it was nearly always in CW or First & as a result of that wild horses couldnt make me fly long haul economy again, Mrs ABZDisneyFan is of the same mind, which is why we have become expert at collecting avios as they allow us to fly at the front of the plane without paying the eye wateringly expensive fares. We also do not have kids so are free to travel outside of school holidays but I know plenty of people who regularly book reward flights in WT, WT+, CW & First for their whole family during school holidays so it can be done.
Apologies for the long rambling nature of this post, if you have any more questions about using avios with BA please feel free to PM me.