Help me avoid my neighbor please

Mommaof4

A few months ago, we moved very far from friends/family, we rent a house in a small tight-knit community. The good part is, it's been really easy to meet people, as everyone knows each other, have events etc, so we've been introduced easily. The tricky part is everyone knows each other's business, so you also have to be careful socially.

We were becoming friendly with another family down the street with kids close in age to ours. They were very welcoming, invited us over a few times, but something about the woman was just rubbing me the wrong way. I was getting the sense that she was interested in my husband, and other behaviors I felt I cant trust eg discussing others' business. So I decided it's best to distance. Like say hello if I see her at the park, there was an engagement party and I said hello and a quick small talk, but dont want to pursue a friendship, hang out at her house etc. We had only been friends a couple months, so I thought this would be fairly easy to do. A couple "Ive been busy" etc and she'd get it, right?

Y'all, shes not getting it. She keeps calling and texting. I will respond once with a "been super busy, hope you guys are well" and otherwise not respond or call back. She asked when can we get together, I didnt reply. They keep inviting us to their house, like 3x, we decline and dont follow up, but they keep asking. We have been avoiding them for 2 months now. This week alone, I have gotten 2 calls, 2 texts wanting to meet up, then her kids knocked yesterday asking if we can join them at the park (luckily I was upstairs not feeling well so my husband told them not today) then her husband called mine last night inviting us to come for lunch Saturday. It's getting super awkward always finding excuses, and the kids' park is right by their house and I find myself avoiding it. I thought usually after a couple avoidances, people are like "ok, ball is in your court" and back off. And we had only been friendly for a couple months, a small handful or get togethers, it isnt like they are long term friends so this is super uncalled for of us.

I am hesitant to be direct because everyone here is so close knit, and we are becoming friendly with a couple other families who are friendly with these people. We are bound to see them around, there are always events and kids bdays etc... fine by me, I will be courteous and say hi, but I want to leave it at that. I dont want to create hurt feelings or drama by confronting her, as others will know about it too, and Im not looking to be ugly towards her either.

Any ideas of what else we can do?