for better wifi there are loads of solutions, not necessarily mesh
simplest is a freestanding wifi booster that plugs into a power socket
if you can run a rj45 cable to your existing router, add a wireless access point near the door and wire it back to your router
if the problem is mostly around the door, can you add an external wifi access point and power/wire it through the wall eg into a garage?
for mesh, there are plenty to choose from, from the well known suppliers eg BT, google, linksys