This might help. Although you might have to re-align some points at the end.
- Using the align menu make sure you have selected the option "align to Selection. Then with the (A) arrow select two points of the total four points you want to join.
- After the selection choose first alight vertical and the horizontal (to be fair, it doesn't really matter which one you do first as long as you do both.)
After this repeat the same steps to the last two points/corners you wish to join together.
If this messes a bit up with the rest of the lines you can use the same technique to make a horizontal aligh or a vertical align in case you need. Also you will be able to select the joined points now and move them as you need and you just know they are not separate nor overlapping.
Hope this was clear enough :)