Cross bites like that make take a little longer to fix but it is totally doable. We push the lower canine in and push the upper incisor out. And the aligners keep your teeth apart while the teeth are crossing paths so it works really great.
Invisalign can do a very nice job of correcting crossbites, as long as they aren't too severe. When they become severe, the amount of time involved becomes so large that alternatives are a better option.