You are correct, and that is why some people will put each property in a separate LLC. Some states have series LLC that in theory will protect each one individually, but there is no case study on it yet.
To protect your business assets if you were to be sued individually for something unrelated to RE, you should look into creating an LLC in a business friendly state such as WY or NV. These states have laws that put in place a "charging order." The charging order prevents a judge from allowing a plaintiff to come in and just sell off everything for your money.
Disclaimer: If you were to receive a judgement, they may still be entitled to disbursements made to you from the company, but there are other ways to work that.
Also, you should not hold your LLC as 100% owner if at all possible. Set it up 50/50 with your wife if possible.
Also, with your LLC being in WY or NV, these states do not disclose members of an LLC, which would make it quite difficult for an attorney to track down exactly what you own. Plus, they would have to hire an attorney licensed to practice in WY or NV.
These different steps are not 100% guarantees, but they act as roadblocks to an easy lawsuit for an attorney. By setting these steps up, you are basically putting up a lot of red tape in an effort to discourage an attorney from pursuing a case.
You definitely want to have insurance policies as your first defense, but legal company structure is extremely important. If you would like the name of an attorney that we use, let me know.
Plus, be sure that your LLC has all the proper documents in place that would prevent someone from "piercing the veil" For an LLC to identified in court as a legal entity, there are certain required docs including operating agreement, proper articles of organization, disbursed ownership certifications, etc.