I don't think there's a solution to what you're after. I don't think there are any single-lens solutions that do wide angle, long zoom, low light etc etc. You need to manage expectations and you will probably find you don't need as long a zoom as you think you do anyway because it seldom generates interesting shots in a general walkabout/holiday context. You'll look back at photos and realise all you've got is up-close shots of distant stuff you don't care about simply because you could get the up-close shot.
I use a Panasonic GX80 with a Panasonic 14-140 f3.5-5.6 lens. The lens is slow, but because the dual image stabilisation is very good I get away with indoor shots, but I'd not use it in a genuinely low-light situation. For that I have a Panasonic 25mm F1.7 prime lens.
With that said, I think you should get a MFT camera with a lens to get you going and buy a prime down the line so you can get better indoor shots later on. A quick glance at MPB, I'd say get the EM5 mk 1 for £224 and a 14-42 kit lens/Oly 12-50/Panasonic 12-32 (best of the bunch, lowest zoom range). Remember you can crop images at home to get a more up-close photo of your kids without sacrificing too much - 16mp is enough to let you do that.
Good luck with whatever you end up with - should beat your phone easily
I use a Panasonic GX80 with a Panasonic 14-140 f3.5-5.6 lens. The lens is slow, but because the dual image stabilisation is very good I get away with indoor shots, but I'd not use it in a genuinely low-light situation. For that I have a Panasonic 25mm F1.7 prime lens.
With that said, I think you should get a MFT camera with a lens to get you going and buy a prime down the line so you can get better indoor shots later on. A quick glance at MPB, I'd say get the EM5 mk 1 for £224 and a 14-42 kit lens/Oly 12-50/Panasonic 12-32 (best of the bunch, lowest zoom range). Remember you can crop images at home to get a more up-close photo of your kids without sacrificing too much - 16mp is enough to let you do that.
Good luck with whatever you end up with - should beat your phone easily