Any invitation is issued under the name of the person or couple hosting the event only. If you and your second wife are hosting the rehearsal dinner, the invitations read "Mr. and Mrs. Robert Roe," and the groom's mother's name does not appear at all. If the groom's mother is hosting the rehearsal dinner, the invitations read "Ms. Jane Doe," and your name doesn't appear.
Parents who are guests at an event often complain that this format "means" that they're not considered a parent because they couldn't or didn't contribute financially. Nothing could be further from the truth. If your son's mother is a guest at the rehearsal dinner, you will give her every honour due her as a mother: advantageous seating, a corsage if other female relatives have one, an early opportunity to toast if other relatives are toasting, and so on. However, she will not receive RSVPs, and she will be free to talk to her friends and family instead of greeting guests and making them comfortable, as she is not the host. In short, she will be honoured as your son's mother, without being expected to do any of the work of hosting a party.
Both sets of names-"Ms. Jane Doe" and "Mr. and Mrs. Robert Roe"-only appear on the invitation if both parents are hosts. This doesn't necessarily mean that both parents are financing the party, only that both are doing the work of making it successful.
A married couple typically entertains as a couple. If your son's mother is complaining that your wife's name shouldn't be on the invitation because "she isn't his mother," she's out of luck. If you give a party, your wife is automatically the hostess if she's present.
Use the formal title that the specific individual prefers. If your son's mother calls herself "Mrs. Jane Roe" (retaining your surname and the married title), then it is improper for you to refer to her as "Ms. Jane Doe" (her maiden name, with a title she dislikes). The only name you can refuse to let her use on this invitation is "Mrs. Robert Roe," as divorced women never properly retain their ex-husband's full name. Otherwise, humour her and use what she prefers.
Formal invitations are used only for formal parties. Unless the planned event is a sit-down dinner at a nice restaurant, you can avoid the entire issue of names and titles by using a more casual invitation format. For an informal party, it's equally appropriate to write:
"Come celebrate and relax with Betty Bride and John Roe after the rehearsal.
Join us at [time, date, place]. RSVP to [parent who wants to receive RSVPs]."
When people start squabbling over who is "really" the host and who as the "right" to be listed on the invitation, the time has come to switch to neutral language and skirt the issue. It's also appropriate to start a formal invitation with "The groom's parents invite you..." without getting too specific about who is and is not a parent. It's also possible, if you're using a very formal invitation, to simply write:
The "honour" or "dishonour" of being included or excluded on a rehearsal dinner invitation will be forgotten by all but the warring factions before the dinner even takes place. The memory of family tensions at the dinner itself will linger in family legend forever. If the issue becomes contentious, volunteer to be the bigger person!