Sorry to be the bearer of bad news - what you want doesn't actually exist.
If you want an all terrain - you have to go big and bulky. The suspension and the large wheels that make them able to handle all terrain are also what make them heavy.
If you want a light and compact - you have to go for city stroller. They don't have the same wheel base nor suspension in order to make them fold neatly and stay light.
If you want to see what I mean take a look at the difference between a bugaboo bee (a city stroller) vs a bugaboo fox (an all terrain). Just look at the wheel size difference.
The only workable hybrid is a 3 wheelier - such as the baby jogger - now this would suit you perfectly but it's not really suitable for a newborn and they don't come parent facing. So they are better suited to older babies - imo.
You could look at the uppababy cruz - I've not tested one but could be an option.
With your dilemma though alot of people just have to have a second stroller.
I'd suggest investing your money in the stroller you're most going to use and getting a second hand one as your other.
E.g get a good quality city compact or mid-range travel system, something that works for you day to day getting in and out of a car and get a second hand all terrain like an Uppababy Vista. The uppababies are built to last. They are excellent quality strollers that can take a tonne of pounding, so they come up frequently second hand on Facebook market place etc and still have years of life left in them.
There's a place called 'buggy pitstop' that can completely revamp a second hand pushchair to near new condition. They will collect it via courier and send it back to you (unless you live near Harrow and you can drop it in).
Hope this helps! YouTube has a tonne of reviewers - magic beans, the stroller workshop, the baby lady and more, so also a good place to start your research xx