1. CLAIM vs ticket, to insurance company, CLAIM is worse than ticket. A ticket causes them nothing except they have the excuse to increase your insurance (because of your insurance rating). Your LP has two claims in the past, and if insurance company considered those were her fault (even though there was no ticket), she is considered by insurance company as "高危",not you. What, and how much was each of your LP's claim? That maybe a lot.
2. When you renew your insurance, your insurance company will probably provide each insurer a rating, look at the rating of your LP, and all insurance companies have access to that information. A bad rating will stay there for quite long. (probably seven years at least)
3. I think, in the meantime, LZ better renew your insurance to monthly payment, when you find a company willing to insure your LP, switch to that company. How to find insurance company is tricky, hence I would like to suggest to you hire an insurance broker to shop around for you and your wife. Maybe you can try Statefarm.
Good luck