You should report this loss to your insurance company. You should provide them with accurate details including the fact that your wife backed into your car. Some insurance companies will waive your deductible if both parties are insured by them such as you and your wife.
Each insurance company analyses your driving record and claims history differently. Some will not impose a higher rate if no record of this is made on your driving record. It is unlikely that any record would be made since it does not appear as though anyone was issued a ticket. On the other hand, some insurance companies look at your claims history in addition to your driving record and as result may impose a higher premium if your insurance company pays out a claim.
You can see how we can get you insurance cheap by getting a car insurance quote here.