If you integrate it then it stays with the house if you ever sell

I can't see from your sketch whether your design incorporates the table or not; I think it might. I think you can integrate it and still take it with you if you do so cleverly. If it is inset into the butcher block (i.e. surrounded by) it'd be difficult to remove and have the kitchen look normal. But if you butt the two against one another in certain ways (a butcher block the same length of the table for example) it could work. Don't forget that it is increasingly common for islands to have two different height surfaces. Usually the kitchen side is shorter, but that need not be the case.

Of course, if you're never leaving the house, don't care to lose the table, or don't care what the buyer thinks, then make whatever design you want!

Separate, gain use of the fourth end/side. Don't attach . If you are planning that as a t at the island end as I think your photo is showing?.......no, not loving that, and a lot of storage taken away in the island size.

I guess I wasn't clear- I would either butt the table up to the side of the island, OR not use it at all, and just extend the counter top to make a table. Mom's table would never actually be attached to the island. I'm going for what looks better, here. I can use her table as an art table elsewhere if it isn't a dining table.

Well I don't think you can butt it up to the island because of the reverse L shape or integrate it into your island, but looks like there is room for it in your space. Since you don't show your other finishes, I can't tell if it would work or not.

the "table", be it mom's or just extended counter is drawn on to the island already, the 3x5 extended section. there's no room elsewhere. the rest is living room space.

I am designing to resemble these spaces. white Shaker cabinets, butcher block countertop tops, wood floors, apron front sink

Got it! So no. You could push the table up to the front of the island to get two or three on each side but that might intrude on what you consider your living room.

I wouldn't use the table as part of your island, but to create an actual island to add chairs to. Put the fab table somewhere to shine though.