Flown several times with bmibaby and more than happy.
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Last time was 3 weeks ago and I think we were delayed about 20 mins, but they made the time up and we landed as scheduled. Seats are allocated at check-in, so you don't have the mad rush like you do with some airline carriers e.g. Ryanair or Easyjet.
Personally I prefer unallocated, as being a lone traveller I can usually find a window seat. So far, whenever I've flown with an airline that allocates the seats I've been stuck on the aisle side
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! However, this will be better for you because of the children, you won't have the stress of wondering if you'll get seats together.
Regards
Louise
Ps The sooner you book it, the sooner you can start looking forward to it