Tell them you will do either but your rate is 50% higher to work on site.
For long term contracts it is better to stick to constant daily rate, whatever you are on site or remote, as this makes companies planing and accounting easier. Of course it is fine to charge for travel expenses but that should be also agreed upfront.
Depending on work arrangement your costs may be even higher with remote gig - work space, utility bills, software licenses, hardware, occasional travelling, accountant etc.
You misunderstand. Remote is the normal salary you want. The on site salary is normal salary + 50% inconvenience fee.