Budget?
Honda CRV comes to mind - not luxury per se but get a top spec model (i.e. EX) and it will all the toys you need. No street cred so unlikely to attract unwanted attention. Should be able to cope with 2 kids + dog and anything else you can chuck at it. Should be fairly reliable and decent running costs.
The taller body really helps with ingress/egress and especially if your children are in car seats - I also find that the sit-up straight driving position more comfortable on longer runs than the sat-low, legs out position in most estate/saloon cars.
I've currently got a Audi A6 and keep banging my head getting in, same with my previous BMW 3 series and I'm only 5'10" - much refer my Landcruiser in that respect.