We were refused our first application for visa so we are reapplying.. Do I mention the first refusal?
It shouldn't be necessary to mention this unless you are asked. If there is a place on the form which asks you whether you have already applied and been refused you will have to fill that in, but if there isn't you don't have to make a point of mentioning it. They should have a record anyway, so the authorities will already know about any earlier applications you have made (that's one reason why you really must tell the truth if you are asked, because they will easily be able to check).
Do you know why your application didn't succeed last time and if so, has the situation changed? If not, there could be a problem this time too. You may wish to contact the agency/ office etc which handles visa applications for the country you are trying to enter, and check with them that you have everything you need. Good luck.