If they’re only planning on staying in that house for a year or two then I can totally understand not wanting to spend a lot on redecorating, that makes sense. what doesn’t make sense is wasting money redoing things that are perfectly lovely and functional. Is a grey kitchen really going to improve her life? Are quartz counters going to make her days easier? Is a wooden floor going to make her happier? No, no, no.
Absolutely spend time and money on the kids rooms, it’s their first time moving house so do what you need to to make them happy and settled, definitely go ahead and remove things that are broken or hideously out of style. That house was fairly neutral to start with, nothing offensive at all. Maybe change the patterned wallpaper if that’s not your thing but Sarah is planning a full on renovation...with a loft conversion.