OP I'm a professional gardener.
The gardens you picture in those photos are the kind of gardens I create and tend for people who want low maintenance.
The crowded planting means no weeding.
The hedges and shrubs need pruning once or twice a year. You could pay a gardener for a couple of days of work a year to do this.
The flower borders you have will just need a simple chop once or twice a year. Your gardener could do that. If I came in to do your topiary, hedges and borders for a couple of days it would charge you about £180 a day. I'm in the South West and am not the cheapest gardener here by far.
Whilst your children are young you might well want lawn. You could ask someone to create this for you, but perhaps a small area of garden - just enough for play. I'd strongly advise against taking the whole garden to grass for three reasons. Firstly most onerous and repetitive task in any garden is mowing. Week in, week out from March to pretty much December now. On a big scale this is a morning's work for someone every weekend/every other weekend.
Secondly, your children will only be ball mad age for a short time. When they and you are older you will almost certainly prefer looking at beautiful borders rather than mowing away 25% of your weekends. It would cost you an absolute mint to replace borders of that quality. If you just create a bit of lawn now then when your children grow out of it you'll be able to replace it with something else. More veg beds perhaps?
Thirdly, that garden will be buzzing with wildlife. Your children and you will love seeing the year play out....birds nesting, bathing in the bird bath, toads, hedgehogs....honestly, it will be a joy.
Being really blunt, there is no such thing as a no/low maintenance large garden.
Even a small yard of chippings needs weeding regularly.
If you really don't want to garden then a big garden is a bad move when you are working and young children take up so much of your time. On a long term basis it's a nightmare. Most of my work is for people whose gardens have become too much for them, older people who now have to find a way to afford me every fortnight. The pressure and worry on them is a burden I wouldn't wish on anyone. Really think about this before making a rotten rod for your own back.