Two Apple ID's are not required to separate the text messages, but two email address are.
It is easy to do if you and your wife each have your own email address. In Settings->Messages->Send & Receive you will find a list of the email addresses associated with your Apple ID. Make sure that both your and your wife's email address is listed. On your phone de-select your wife's email address and on her phone de-select your email address. You should also scroll to the bottom of the email address list and make sure that the email address used to start conversations is correct on each phone.
Please note, that anytime your wife wishes to receive iMessages sent to you all she has to do is check your email address in her list and vice versa. Using the same Apple ID allows this. If you wish to totally separate the iMessages then you will need separate Apple IDs.