You can’t have two category fields on one blog form but here is the best resolution of this issue, in my opinion:
Edit your post form
You can include only one category field on your form
Edit the Category field.
Open the Advanced Options area.
In the “Type” box select “Checkbox”.
Save your edit.
Now when you or your subscriber opens the blog form on the front end to create the blog there will be seen a printed list of all of your categories on the blog form wherever you placed the category field. Each category on the list will have a checkbox. The list of categories will have the SUB categories INDENTED from the PARENT categories. You can select any and all categories on this category list as search categories for the blog.
When you build your original category list in the admin backend you can have as many PARENT categories and SUB categories as you want. That is where you can set up your two PARENT categories and their SUB categories as you want them to be.
I would suggest that you build an explanatory comment into your blog form to request that the user select one or more SUB category from each of the PARENT categories or something like that to solve the problem of having two separate category groups.
In the blog form the categories will all be in one long list but you can ask your subscriber to select from that list however you like. Remember these categories are all just a way to search for blogs under a specific subject (category) so it is up to the subscriber to select the right search categories on their blog post so that other subscribers can find the post. It’s their job to get it right…