There is no problem with alternating Botox and Dysport treatments, or for that matter, having both of them done at the same time. Most people prefer to stick with one or the other, but it is fine to alternate.
There should be no problem whatsoever in alternating Botox and Dysport assuming that both toxins work well for you. Some patients have used Botox for a long period of time and are brand loyal because they are happy with the results. Dysport gives equivalent results at a slightly lower price.