I would love to have a round d/r table. We've now entertained for 25 years on the rectangular table we purchased before we actually entertained! I usually do most of the holidays, and I curse it at each occasion:))). More so after I saw a beautiful round d/r table in an antique shop in New Orleans in the late 90's. I would have purchased it, but DH doesn't think our room could have supported the size of the table we saw. That particular table seated 12. No leaves. The round is just beautiful. Like the link posted, it is more functional all around. The seating at a round table makes for easier conversation, you aren't yelling down to the other end of the loonnnggg table. Also, IMO, round is much more interesting decoratively speaking. Post a pic if you do decide on the round, I'd love to see what you have chosen.

The biggest mistake I ever made was buying a round rug to go under a round table. I have an almost perfectly square room with a round table, so I thought round rug, right? Even though the rug was 24" larger than the table on all sides, we still found ourselves scooting our chairs off the edge. I replaced the rug with a square and we are much happier.

Ideally allow at least 3 feet for each chair (2' chair depth + 1' to get in and out). So if you have a 12' space, 6' might be taken up by chairs. That means you can fit a 72" round but wouldn't have a lot of extra space. The leaf would make it really tight. I'm all for extra space, but I fell in love with a round table, so I will deal. I have an 8x8 space plus walk room on one side, and I picked out a 48" round table. I have no extra room on some sides but the roundness helps. There are a lot of options. I would go into a showroom and ask the sales associate for help. There are convertible tables, thin pedestals, variable tabletops, exterior and interior legs, 3 legged tables in addition to leafs. Sorry that was probably not much help. I went into a crate and barrel showroom and asked for help and I was able to figure out what I wanted through the process of elimination. They have enough different configurations that you can get an idea of what will and will not work in your space. I would optimize floor space for your family and only add the extra tabletop space when you absolutely have to. The chairs make a big difference in how much space you have around the table when not in use. You can choose uncomfortable chairs that fit tightly against the table (if the table allows) or comfy upholstered chairs that take up more space when pushed in as much as possible. If you go rectangular, you have the option of benches. They have upholstered benches too. Every inch matters. If you can trim a few inches off the chairs or table edges or scooch the chair under the table a bit more, you may be able to come up with another 6-8" around the table. This one says it will fit 6-8, but I wonder if you could get more kids around it if you use benches. (It's not the most attractive IMO.) Table goes from 34x57 to 57x68.

https://www.globalfurnituregroup.com/ca/healthcare/products/tablet-tables?tab_active=images An “add-on table” might work for the end of your dining table. Turn it as you intended so it is under the ceiling light, remove the two stools and the floor lamp.