With that size bathroom, use small scale vanity and just shower. Is bath room open to kitchen? Need a door separating the two spaces. Eww!

Here is a actual picture, if you refer to the first drawing the kitchen is labeled kitchen.

I am planning on using the space outside the kitchen and bathroom as a utility/office room

Actually that’s why I was thinking of positioning the laundry closet as drawn in the diagram so I could install a door between it and the bathroom which would provide two doors between the kitchen and bathroom.

my question is if I place the door center of the wall opening right, towards the tub, with the toilet directly across from the doorway will I have enough room for a 60inch vanity on the wall that is opposite the tub.

So the 60 inch vanity would run on the opposite side of the room as the tub on the 5ft wall. With the toilet in the middle directly across from the doorway.

Does anyone know if that would work or be best in this situation?

Yes, you would have enough room for a vanity across the room from the tub. If you are short on storage I suggest using a linen cabinet or build in a small linen closet and using a narrower vanity. If you are going to have double sinks, that is a good reason for a 60 inch vanity but otherwise, think about improving the storage

I am not sure about required door width for a bathroom, but practicality suggests a 30 inch door. Even though all occupants may be able bodied and planning to stay that way, fate has a way of interfering with plans. A narrow doorway would be a problem for a resident, or visitor, with mobility problems or otherwise needing assistance. If someone is trying to rush a sick child into the bathroom, a wider door would make it easier and be less likely to end up banging an arm or leg on the doorframe. Many old houses have 24 inch doors but why not upgrade this aspect to the current era?

I am planning a bathroom with this exact layout that hou describe and the same 5x9 dimensions. are you happy with this layout and is the design working well for you?