Several ways to deal with this:
Underpromise and overdeliver.
Don't give hard deadlines with job start dates - "we are looking at the week of the 10th, unless weather or anything out of control holds us up".
You could also explain to the current customer that all the things they want done are not in the scope of work, and that you have other people locked into firm deadlines, and then suggest drawing up a new contract/proposal for the new work and scheduling it after everything else.
Underpromise and overdeliver.
Don't give hard deadlines with job start dates - "we are looking at the week of the 10th, unless weather or anything out of control holds us up".
You could also explain to the current customer that all the things they want done are not in the scope of work, and that you have other people locked into firm deadlines, and then suggest drawing up a new contract/proposal for the new work and scheduling it after everything else.