Upvote:1
Yes, your mother can travel to UK on her own, as dependent in this case means financially, and both of your parents would be issued their own individual visa.
Each person files a separate UK visa application, although their applications can be linked when filing as a family so that only the primary would need to submit financial evidence. The Supporting Documents Guide gives the details.
However, both applications should state their separate plans, that your mother would stay for 2-3 months, your father for 2 weeks at the end of that period, and that they plan to return home together.