Lets start with the merge.
You cannot delete anything without changing commands.
I assume that your DVD is split on a Title. First DVD has menus and first half of title, second has second half of the title only.
When you do merge, merged DVD will add all VTS from second DVD plus VTS with a default navigation menu.
Default menu has choice of two DVD to play. If you click on first DVD it will go to a menu in that DVD, assuming that how the first DVD was working before.
If you click on second DVD in default menu, it will start to play second half of the title, assuming that how it was working before when you inserted second DVD into the player.
You can use Debug to see how merged DVD functions.
If you want to bypass default menu, you can change command in First Play to jump to a Root menu of first DVD, which will get you to your main menu.
Easy way is to right click on VTS which contain Default menu and click on "Hide all blocks". That will bypass it and get you to a main menu in first DVD. That is the first step.
Now you will have to change command at the end of first Program PGC to navigate to a second half which is in different VTS.
To do that add PGC in VMG Menu and use Jump/Call command at the Cell or Post Command section of first title to go to that PGC. Than Pre Command in that PGC will be Jump to a VMG Title #, where number is a number for second Title. You will find corresponding number if you click on VMG Titles.
Now add one more PGC in VMG Menu and change command at the end of second Title to go to that PGC.
Pre Command of that PGC will need Jump to a VTS Menu which will be your Root menu of the first DVD.
I added two PGS just to make it simple, because there are PGC made by merge to navigate between those two DVDs, but you will have to look for them.
If you have Chapter menu to navigate second DVD, it may get little more complex, but we get to it after first part is working.
Do not delete anything.
Second method is easier, especially if you have to deal with chapters, because they are in the same VTS.
It may not play the way you did it because there can be a command in last Cell of first DVD to stop the play to insert second DVD. That you have to see and delete it, also make transition cell seamless.
You have to edit Title to add additional chapters from second DVD to match and check on Post or Cell Command in Program PGC that it go back to a menu at the end of play.