Pushing Settlement Date - what rights do we have?

My partner and I were living on a 3 hour round trip drive from where our work and family were so we sold our house, moved back in with my childhood room with our 3 cats and 1 dog temporarily while we have been looking for properties closer to here

About 90 days ago we found a property we fell in love with that was up for a 30 day settlement within our budget. When we did the second inspection they suggested it would be more like 60-90 days, which we also agreed with as we loved the property - what's another month at home?

Once we finally signed the contract it was pushed again to 120 days which we begrudgingly agreed to. We're in the home stretch now and we're finally on the last 4 weeks before settlement

REA reached out last week and asked if we could push it another 4 weeks, we said no. Now our conveyancer has reached out to us and said the vendor wants to push it 4 weeks because the family she was moving in with has 'left her in the lurch' but that story has also changed multiple times since we've been waiting to move in

The vendor refused to leave for us to inspect the house the first time, just kind of hid around the corner. Refused to leave for the second one and followed me around the whole time not really letting me look at anything, refused to put her small birds into their cage when we tried to inspect the bedroom. Did not want the building and pest guy to come and do the report

I'm waiting to hear back from my conveyancer and I'm stressing hard - do we legally have to extend?? We're dying to move in D: