Double wells, by Evans M. Harrell, Comm. Math. Phys. 75, 239 (1980), should be sufficiently rigorous. The result for the tunnel splitting, theorem 2.22, applies to a symmetric double-well potential in arbitrary number $n$ of dimensions, constructed as the sum $V(x-f)+V(x+f)$ of two single-well potentials $V(x)$, bounded and of compact support, after translation by $\pm f$.
The tunnel splitting is given for large $f$ in terms of the eigenfunction $\Phi(x)$ for the lowest eigenstate in the potential $V(x)$, $$E_1-E_2=\left(\int\Phi(x-f)[V(x-f)+V(x+f)]\Phi(x+f)\,dx\right)(1+o(f^{-n}).$$