AFAIK the Three upgrading is aimed at boosting speeds but not improving coverage so I doubt whether it’ll help you.
Years ago I used a repeater to boost the Vodaphone signal in our large, thick-walled house.
It worked very well and was only £25 but isn’t the right frequency for Three who use 800MHz (Band 20) and 1800MHz (Band 3) for 4G and 2100MHz (Band 1) for 3G. If you want a repeater you’ll need to find one that does 800/1800MHz but a trawl through Banggood, eBay and AliExpress should find some.
EDIT: Banggood do one for £75. Takes 10-15 days to arrive. Choose option “E”
HERE
Another point would be to check what bands your mobiles use. Not all phones have all the bands so it’s possible that you may be missing one of Three’s frequencies.