Oh boy - this is the problem with small companies that don't understand a thing about HR.
While you have these 2 women who are stirring up trouble, someone's buying into it either because they agree or because they are sick of the matter landing on their desk. So the VP may be making it easier to him by trying to get you to scale back. Assuming you have double-checked your own behaviors and see if there's any way you could, or should, scale back the personal stuff done in sight of others (making the lunch dates, happily chatting on the way out to lunch, chatting about what the friends did last evening or last weekend) so you don't rub their noses in it, I think you have to continue to go the purely-professional route.
I would ask the VP to put in writing exactly what the company policies are regarding what employees do on their own time. Ask that the company spell out in no uncertain terms what the dictates are regarding lunch, dinner, weekends, as well as business travel or errands for work. Ask that it be distributed to all employees so that everyone knows the policy, including definitions of "personal relationships" and what the penalties are for violations, either planned or inadvertent crossing of paths in outside settings. Say you don't know what the laws are but you are sure the HR person or the VPs or President have access to an employment lawyer to provide the wording. Ask also what types of conversations are permitted and prohibited. After all "How was your weekend?" or "Have a nice holiday" could easily be construed as personal conversations. (This should make it obvious that what the VP is doing is completely illegal, without you saying so.) You can note that you have been promoted and well reviewed for your work ethic and performance, and you want to be crystal clear (and have others be clear) about every single policy, including this one. Ask that the written directive also include reporting requirements if anyone is observed having this sort of prohibited relationship or conversation (which will of course include the 2 trouble-makers). I think your tone has to be "Help me to understand the policy, what it covers, what time frame it covers (9-5? 24/7), who is exempt if anyone, whether it covers things like charity events (what if a bunch of people sign up for a 5K or a food pantry collection drive?), how this impacts company productivity and profits, and ideally what the rationale is." I realize this is completely stupid but I don't know how else you can approach it.
You can consult an employment lawyer, of course, but if you are in a small office where it would be easy to demote you or make life miserable for you, and if you have no HR resource worth talking to, you could push yourself out of a job.
I do think the employer has the right (as petty as it may be) to say that office time, office emails, etc. should not be used to set up social arrangements (with employees or with other friends/ family), personal calls are banned, chatting at the coffee area is not allowed, etc. It doesn't build company camaraderie, but then there's a big chunk of that that's missing from this office anyway.
Otherwise, I think you have to either be very secretive with your coworkers, or you have to think about looking for another job. What a last resort that would be.