I would pre book private taxi/transfer. "PennyW" who frequents this site has recommended one or two in the past, one of which I think is Parkers. Hopefully Penny will supply more information.
A taxi/ minibus will cost around £45-£50 so unless your children are very young combined rail fares could well be close to that
Go for a well established. Chester firm such as KingKabs or Abbey Taxis ( niot an endorsement as have never used either for airport transfer) Check carefully as some firms who quote cheaper fares wait for other arrivals to fill up the minibus to keep costs down so you could be waiting around the airport for a couple of hours
There are specialist airport taxis which would be better value than KingKabs or Abbey Taxies though I see they advertise Airport transfers. We used to use Parkers which were excellent, I think they are online nowadays, but we prebook parking and drive ourselves now. The train will involve a change at Crewe or Manchester and if there is a gang of you more hassle than it would be worth.
I used Omega Transfers in April to get from Liverpool to Manchester Airport which cost £50.
I thought they only operated out of Liverpool, but looking at their website it looks like they might operate out of other places in the North West.
Might be worth getting a quote from them.
Speedie Cars are good value so may be worth a try - 01978262829 - http://wrexhamtaxi.co.uk/. We paid £48.00, but I'm not sure if it would be more for 5 passengers.
If there are five of you with bags you will probably need a mini bus or people carrier rather than car.
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