If it were me, I would want the contract to require several thousand dollars to be held in escrow following closing, and payable to me as a penalty if mom wasn't out on the sixth. I would also serve mom with a formal notice to quit on the day of closing so as to minimize the amount of time she could stay in the home before I could commence eviction proceedings, assuming she did not move out on the sixth. Actually, I might consider moving the closing date to August 6th, so it's entirely the seller's problem.

If you want the lawn mower and snow blower, negotiate a purchase price. The fuel? I would welcome her to get a siphon hose and take it with her, but if you can quantify how much is left and you wish to do so, you can consider paying her for that amount. (Why would she think that you would want to pay for fuel she has used?)