We developed an enhanced Kalman‐based approach to quantify abrupt changes and significant non‐linearity in vertical land motion (VLM) along the coast of Chile and the Antarctic Peninsula using a combination of multi‐mission satellite altimetry (ALT), tide gauge (TG), and GPS data starting from the early 1990s. The data reveal the spatial variability of co‐seismic and post‐seismic subsidence at TGs along the Chilean subduction zone in response to the Mw8.8 Maule 2010, Mw8.1 Iquique 2014, and Mw8.3 Illapel 2015 earthquakes that are not retrievable from the interpolation of sparse GPS observations across space and time. In the Antarctic Peninsula, where continuous GPS data do not commence until ∼1998, the approach provides new insight into the ∼2002 change in VLM at the TGs of +5.3 ± 2.2 mm/yr (Palmer) and +3.5 ± 2.8 mm/yr (Vernadsky) due to the onset of ice‐mass loss following the Larsen‐B Ice Shelf breakup. We used these data to constrain viscoelastic Earth model parameters for the northern Antarctic Peninsula, obtaining a preferred lithosphere thickness of 115 km and upper mantle viscosity of 0.9 × 1018 Pa s. Our estimates of regionally‐correlated ALT systematic errors are small, typically between ∼±0.5–2.5 mm/yr over single‐mission time scales. These are consistent with competing orbit differences and the relative errors apparent in ALT crossovers. This study demonstrates that, with careful tuning, the ALT‐TG technique can provide improved temporal and spatial sampling of VLM, yielding new constraints on geodynamic models and assisting sea‐level change studies in otherwise data sparse regions and periods. Plain Language Summary: The difference in sea‐level records from satellite altimeters and coastal tide gauges can reveal the Earth surface's vertical land motion (VLM) and potential errors in either system. Time‐varying changes in the VLM can occur because of phenomena such as earthquakes or glacier melt which changes the mass load on the crust. We developed a flexible data combination framework to use records from multi‐mission altimeters (ALTs), tide gauges (TGs), and GPS sites to allow the estimation of substantial non‐linear VLM that complements the previous estimates which can be sparse in the 1990s especially. We considered the study period since the launch time of TOPEX mission in ∼1992. We used our new approach to investigate the earthquake‐induced deformation at TG locations along the near‐coast subduction zone in Chile that could not be inferred from temporally and spatially sparse GPS records. We also provide insights into the rapid change in VLM at coastal TGs in the Antarctic Peninsula after the Larsen‐B Ice Shelf breakup in ∼2002, where the existing knowledge dates to ∼1998 from only one GPS at Palmer station. These significant insights into present‐day deformation help to fill the knowledge gap from GPS‐inferred records and improve VLM sampling across space and time. More generally, this new approach may assist resolve complex VLM for sea‐level studies globally and could add new constraints to inverse geophysical modeling, especially where GPS data are sparse in space and/or time. Key Points: We developed an advanced Kalman approach to estimate highly non‐linear vertical land motion using altimeter, tide gauge and GPS data, while simultaneously capturing significant mission‐specific systematic errorsWe derived new estimates of pre‐seismic velocity, co‐seismic jumps, and post‐seismic velocity at tide gauges in Chile that add additional constraints on the solid‐Earth response to major earthquakes in the regionWe observed the onset of rapid uplift at tide gauges in the Antarctic Peninsula caused by the 2002 breakup of the Larsen‐B Ice Shelf, filling a historical knowledge gap from GPS records and further constraining modeled viscoelastic deformation [ABSTRACT FROM AUTHOR]