Yes , these days it is usual that conveyancing is dealt with by post and e mail. Documents can not only be sent by post but scanned and sent by e mail as well. Any local solicitor to you who deals with conveyancing can assist you with this, including the matter of the youngest daughter's interest.
Each party may feel it necessary to instruct their own legal advisors but only if a conflict arises.Whilst you have a united joint enterprise one solicitor can do the job
There is no need to leave the comfort of your armchair though to go anywhere.
I have just bought a house and never met my solicitor and never been to her, offices delightful as that would have been.