Which is more important to you? Budget means either a terrace without parking or garden, but walkable to a gorgeous park and the high street (good mix of amenities) OR a bigger house with a lovely garden, driveway etc but would need to drive (around 10 mins) to high street/amenities. Good schools in both areas, access to work similar in both areas. 2 kids age 2 and 4.
YANBU driving to places when needed is worth having more space and a garden
YABU driving to places when needed is a PITA and not worth having a garden for