Hello,
If you manage the tabs using multifield then you always has problem with reordering because you are doing node management in code via taking multifield value and when it comes to reordering the only choice you left with to write more node management code to delete and recreate node structure which is very complex.
The best way to handle these type of scenarios are
1. OOTB straight forward way: Create a container component (tab container) which allows you to drop child components (in your example tab) which will be stack. Now you can arrange the UI based on mode type for example in edit mode it will be stack but when you go to preview mode it will display as actual tabs side by side OR you can have edit property in your container component where you can switch between which we you want to view. This way you will have all the flexibility to reorder your node or edit/delete any of tab items
2. Write custom multifield widget which allows you to author multiple widgets in mutlifield. I wrote one already for me. let me know i can share idea how you can do it.
Thanks,
Pawan