We analyse spectroscopic and photometric transits of the hot Jupiters WASP-52 b and HAT-P30 b obtained with ESPRESSO, Eulercam and NGTS for both targets, and additional TESS data for HAT-P-30. Our goal is to update the system parameters and refine our knowledge of the host star surfaces. For WASP-52, the companion planet has occulted starspots in the past, and as such our aim was to use the reloaded Rossiter-McLaughlin technique to directly probe its starspot properties. Unfortunately, we find no evidence for starspot occultations in the datasets herein. Additionally, we searched for stellar surface differential rotation (DR) and any centre-to-limb variation (CLV) due to convection, but return a null detection of both. This is unsurprising for WASP-52, given its relatively cool temperature, high magnetic activity (which leads to lower CLV), and projected obliquity near 0° (meaning the transit chord is less likely to cross several stellar latitudes). For HAT-P-30, this result was more surprising given its hotter effective temperature, lower magnetic field, and high projected obliquity (near 70°). To explore the reasons behind the null DR and CLV detection for HAT-P-30, we simulated a variety of scenarios. We find that either the CLV present on HAT-P-30 is below the solar level or the presence of DR prevents a CLV detection given the precision of the data herein. A careful treatment of both DR and CLV is required, especially for systems with high impact factors, due to potential degeneracies between the two. Future observations and/or a sophisticated treatment of the red noise present in the data (likely due to granulation) is required to refine the DR and CLV for these particular systems; such observations would also present another opportunity to try to examine starspots on WASP-52.