Do I as the seller have the right to know if the bank's appraisal of my home is higher than the appraisal that I had done?>
Appraisals on purchases are the property of the lender ordering them and the buyer paying for them. The only time they are provided to seller is if they come in under sales price and sales contract is renegotiated or voided. Answer to your question is no, value of appraisal is not germane to seller if it supports contract purchase price.
BUT - if the appraisal comes in BELOW the contract price, then definitely show it to the seller, as grounds for your negotiating a lower price!