I think two sessions may be quite difficult, we regularly host big dinners in our not very big house (standard 3 bed semi, but with separate dining room). But the most we have had is 15 and we put two tables together diagonally across the room to fit those in, we do it often enough we have enough tables and chairs but if not borrow them off people and get them to bring them round the day before.
I would put up extra tables in the kitchen & playroom and try and feed everyone at the same time (ish), by strategically mixing the adults and children together, and make it a job of the adults to supervise their assigned children (including yours) as you and partner will be busy.
Give everyone a job to do.. glasses/drinks, serving, supervising, dishing up etc.
I generally cook early/day before and use the oven to reheat then keep everything warm, while doing the last bits and bobs, everything is then placed in the middle of the tables and people serve themselves, it keeps things warm until ready and the 'dishing up time' is removed because people do it themselves, or dish up for others, less hassle and people can have as much or as little as they like then, plus seconds! If you've got three tables you just need to triple everything when putting it in serving dishes, again, we have loads of dishes but if not borrow them before the day before, we find glass/ceramic is best as it keeps warm, borrow if you need to, as long as you prepare what you need in advance you can easily do this.. the problem you are going to have is keeping everything warm, so we find from oven to table and warmed up plates works best.
Or do a dedicated serving table with hotplates and do it like a carvery, look up chafing dishes online which you can keep warm with hot water underneath.
For every dish you need some way of serving it so borrow tongs, spoons & slotted spoons if you need to, make sure you have more than you need, for at least 3 people per table dishing up at the same time.
If you go for a paste table in the kitchen, make sure you reinforce it in the middle!
Good luck, it sounds fab!