Im very biased, so any opinions expressed below that upset people, too bad! also I dont have any kids so feel free to ignore me, the below information has been gathered from watching others struggle for various reasons
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people carriers are a marketing con.. everyone I know with kids has rushed out and brought a people carrier as soon as their second and/or third child was due stating categorically that they "need 7 seats" or "have to have a people carrier as its easier to get kids into because of the height". I even know a guy with 3 teenage kids who brought a cayenne and insisted for 8 or 9 months that they needed the space, blah blah blah, and then got rid because I WAS RIGHT!

He brought my old 545iSE touring and 2yrs on still says "I don't know how we managed before this car" everytime I see him
OK p*ss taking and apologising aside, 7-seater and 5-seater people carriers might seem like a good idea with kids, but..
1.) they have next to no boot space, and what little space they do have is a waste of time as its all in the uppy and acrossly directions.. fine for a picture frame, crap for anything of substantial 3-dimensionality
2.) the only persons i know who regularly uses the 6th/7th seat in their people carrier do so to seperate their TWO children because they always fight if they're sitting next to each other (which to me is more of a parenting issue than a vehicular problem; im sure my mum could fix that one in about 10mins)
One friend insisted they needed 7 seats for their 2 kids (one newborn, one 3yr old), had them installed in their car, then NEVER used them in the 2yrs they had the car. They then went on to buy a fullsize 7-seater people carrier, and removed the back seats and put them in the garage because of point #1 above
3.) they are not economical; my old 545iSE touring with its 4.4 litre 350bhp petrol engine did more MPG than my mates 307SW which had a 2.0 diesel engine, AND the fuel was 10p a litre cheaper!
4.) they do not go/stop/turn as well as a saloon/estate, hence are not safer in my opinion.. I'd rather avoid a crash than survive one
5.) while people carriers high seats are a bonus for getting babies into and out of, they are a pain in the a$s for lifting 3 and 4 year olds into booster seats which they could get into themselves if you were driving a proper car
6.) they are expensive for what they are; for the price of a run of the mill people carrier you could buy a luxury saloon/estate which would cost the same to run and be a 10x nicer experiece for everyone involved
7.) men driving otherwise empty people carriers drive like complete w@nker$, presumably because they feel they have something to prove
8.) women with people carriers see fit to add little warning diamonds to the rear window saying things like "small dude in car" or "little person onboard".. personally I don't care and will not adapt my driving to suit your choice of stickers
Now I've got all that off my chest, my recommendation?!..
Well the E60 touring which I had (and am on the look out for again) is out of your budget by about £1.5 - 2k so, E39 5-series touring in what ever engine/trim variant you see fit.
530i will do 30mpg, 525d will do 45mpg. Ignore the 520i and 520d, they're so slow and use as much fuel as the next size up engines as they're working so hard all the time..
There's enough space in the back to fit a fridge freezer, washing machine and tumble dryer and still see out the back window! They're fast, refined, drive like a dream, the SE's had leather and electric everything as standard, and they're so robust that if there's a nuclear holocaust cockroaches (predicted to be the only living survivors) will be driving around in them because they'll all still work!