My landlady hit my car when it was parked in front of our house. Should I tell my insurance company so that they can go after her?

If your car was parked and struck by your landlady, she should file a claim with her insurance company to pay for the repairs. You can have her pay for the damages out of her pocket, but since the damage is so high, she is better off to go ahead and file a claim. If she has admitted that she caused the damage this should be a simple issue. If she refuses to file a claim under her policy, or denies causing the damage, you can file a claim under your car insurance policy. Since the damage was due to no fault of your own, your rates will not be affected by filing a claim under your own policy. However, the deductible on your policy will apply until the insurance company can get reimbursement from her insurance company. If she fights the claim, it could take some time to get the reimbursement. Of course, if you do not have collision coverage, then you will need to go through her insurance company.