The intermediate after the first step of the reaction is wildly unstable and not at all likely to form. An alkoxide is not a good leaving group, particularly in acidic solution and when there is no strong entropic driving force (unlike in, e.g., the final elimination step of an aldol condensation).
There's also no particular reason to suppose the reaction would follow an SN1 mechanism (you're producing a secondary carbocation only weakly stabilized by resonance with the neighboring oxygen, the substrate is not severely sterically hindered, and the reaction is intramolecular). In order for SN1 to even be possible, it is doubly important to produce a stable carbocation and expel a good leaving group (since SN1 is kinetically unaided by the nucleophile, unlike SN2), and your mechanism has neither. Furthermore, even if SN1 did occur, it would not yield the desired product, since carbocation rearrangement via hydride shift from the adjacent tertiary carbon is likely to occur. Ultimately, an SN2 mechanism is more correct.
Finally, remember what the object of acid catalysis in these sorts of reactions is: to improve the quality of the leaving group by protonating it, thereby activating the substrate to nucleophilic attack. That's where your mechanism should start. Hopefully the rest is fairly obvious.