Local here 🙋🏼♀️ AMA you like about Warwick!
The larger part of Warwick Gates/Heathcote is in Warwick so ignore the PP. It's a CV34 postcode which is Warwick. The Bolingbroke Drive corner is Bishop's Tachbrook, Leamington and the Medley Grove bit is Whitnash, Leamington but the rest is Warwick. But I digress.
If you're thinking Old Warwick Gates i.e. north of Harbury Lane then it's more established and settled. South of Harbury Lane 'new Warwick Gates'/Lower Heathcote is newer and finding its feet. But there are some lovely houses to be found in both.
Hatton Park my plumber says don't touch with a barge pole. The plumbing is a nightmare and a large % of his work is refits there. There's also the South Warwickshire Local Plan which proposed 8k+ new homes around Hatton Park. The Birmingham Road will become an absolute nightmare.
Warwick Gates is just by the M40 so easy to commute to Birmingham. There's also a new junction proposed in the SWLP which will make everything even better.
The flies/smell is particularly bad on Tachbrook Road. However, the Environment Agency is on the case and I do think it's getting better. A US company bought Berry Polymers and they're taking it all very seriously. The extra houses and traffic at Hatton would worry me more.
As a PP says you will have to ferry your kids anywhere that's affordable. Old Warwick Gates has good bus routes.
You might want to consider Hampton Magna as it has lovely walks and is right by Warwick Parkway for commuting to Birmingham. Bishop's Tachbrook has a lovely school but the buses aren't very good.
Schools are tricky as Heathcote was hugely oversubscribed every year until Oakley was built. Bishop's Tachbrook school and Budbrooke school are easier to get into. Feel free to PM me if you have any questions.