i've seen this kind of thing in moderation pretty often. I find the best outcome to be segmentation, so that way you can exist separately, but without directly influencing each other.
Or having dictatorship level control over who you ban and just say "they weren't nice, and a lot of people agreed with me"
Another option is to have a communal vote on their behaviors, and to see what people collectively decide, and act upon that, it's generally fairly productive.
Creating rules unless explicitly needed, is almost never a good idea. In this case i wouldn't create a rule about posting websites, i would create a rule about excessive aggression. I.E. we want this place to be civil, there is no need for people to be starting drama. Linking through 1 site, to another site, explicitly for the purposes of directing engagement is going to be pretty aggressive. Have a problem with people here? Talk about it here. Otherwise go away, you already aren't using this platform for that, it shouldn't matter.
Rules are often very hit or miss. People will often be ok with you just heavy handedly banning someone, because they got on multiple peoples nerves, rather than for violating the rules. You don't need to violate a rule to be banned, you just need to be disliked by the community. The more open you can make this process of heavy handed moderation, the more people in your community will respect it.
Nobody likes a passive aggressive person, people like a passive aggressive moderator even less. Be clear about what you do, and why you do it. It's your platform, you host it, you're allowed to moderate it how you please. You own nothing to anybody else, except for respect (assuming they respect you)
oh and my tip for the week: Don't engage in drama, It's needless. Especially when it comes to moderating communities.