You can move from your conventional IRA plans to self-directed IRA plans. The only difference between such plans is how they can be invested, with the self-directed plans providing options beyond just the stock market.
You and your wife would each need to establish your own self-directed IRA plans. It is possible for those two IRAs to joint-venture to purchase an investment property.
With a self-directed IRA, it is not "you purchasing your first rental home", however. A self-directed IRA is simply a means of diversifying that tax-sheltered retirement savings. The IRA would own the home, all expenses would come from the IRA and all income must flow back to the IRA - just like when an IRA invests in the stock market. You may not personally benefit such as by drawing income from the rental personally, nor may you inject value into the IRA through the provision of goods or services such as performing work on the property.
Basically, you get to be a fund manager and deploy your retirement savings into an asset class you know and understand with these vehicles. As a brand new real estate investor, do you have the confidence that you will be the right fund manager in the right asset class?
There is a lot of great information here on BP on the topic of self-directed IRA plans.
You can pool your respective IRAs in the same LLC and the invest in real estate through the LLC.