My recommendation is that you stay at Reading, which is as good if not better than Exeter, and that you do not dilute your law degree by studying business.
My chambers recruits university-blind, but we prefer rigorous academic degrees to flakey subjects such as business, and I don't think that we are alone in this.
You can learn about business by reading, and by practising law for business clients.
Please note that university-blind recruitment is becoming widespread in law firms and barristers' chambers.
The Russell Group is a marketing group, and the fact that a university is not a member of the Russell Group does not mean that the university is not a good university. Reading is a good university.
To practise in the USA, you would need to pass the Bar exam in one of the States, and have or obtain the legal right to work in the USA. . Possession of a UK law degree makes you eligible to take the Bar exam in New York, amongst others.
PS: Congrats for being one of the very few people on TSR who knows how to spell Russell! Exeter has one r, by the way.