Unfortunately, the Mazda 5 is not compatible with what you want. It's very unlikely to seat all three kids in the back - and it only has two Isofix anchor points in the second row anyway. That leaves you with two options (unless you can think of an alternative model I haven't): 1) a larger car like the Sharan or MPV with sliding doors, 2) a slightly smaller car without sliding doors. You're unlikely to get a smaller car with sliding doors, essentially.

Here are some models that fit three child seats across the back (but not all have three Isofix points):

1)Audi Q7
2) Peugeot 5008
3)VW Touran
4) VW Sharan/SEAT Alhambra
5) Citroen C4 Grand Picasso
6) Ford Galaxy
7) Renault Grand Scenic
8) Citroen C5 Aircross (two outer seats get isofix mounts)
9) Vauxhall Combo Life/Citroën Berlingo/Peugeot Rifter (second row gets 3 isofix points and fits 3 child seats, but the third row with two seats isn't suitable for car seats. It has sliding doors but is obviously much larger than your S-MAX as it's van-based).
10) Volvo XC90