My son is 4 and my daughter is 15 months--so they're both quite close in age to yours. As to your plan being feasible, I think it depends on a few factors.
How much time do you have to spend in the garden? If you're working, you might not have enough time to get the beds made.
How much will your kids play by themselves while you work? If they squabble or keep wanting your attention and don't want to help, you'll have less time. Sometimes my son plays great by himself outside and/or likes to help me. Some days, he just doesn't. And, that's okay! It's just something to take into consideration. Your youngest should now be old enough to toddle around and play without needing to be carried and held and fed constantly, and that will free you up a lot more, too. From birth to when they really get walking, is the hardest time to get stuff done in the garden. It gets more fun and easier as they age, at least it did with my son!
How much experience do you have gardening? I've been at it for almost 5 seasons now, though all of them I was rather divided in time/energy as I had little ones to care for. But, I still wasn't nearly as successful as I would have liked in growing things. A lot didn't sprout, a lot died, a lot just didn't produce. With me, there appears to be a loooong learning curve, as well as the soil needing time to become fertile (at least, I'd like to think part of my problem is my soil!)
I think, if you've got time and nice weather (i.e. not so rainy/muddy/snowy so that you can't put the little one down to play), you should totally be able to get everything accomplished. I tend to get made about 2-4 beds/year. I start building one, finish it, and then start another. It takes time, and you might not have them all done by the beginning of the growing season, but you should have them done by fall.
I would, personally, start by building one bed. Get that one done and then start the next. If you have access to mulch, you can mulch the whole garden area while you work on the first bed. This will help build nutrients in your next beds' areas, as well as keep weeds at bay. Once you've finished an area, you can move to the next. Either remove the mulch or incorporate it it. By building one bed at a time, you get a place to plant some foods--the earliest crops like peas and radishes, as well as some of the kids' favorites. This way, even if you don't get the other areas made, you've got a place to do some growing and memory making, as well some food to munch on. And, since everything else is mulched, you don't have to stress about not getting it all done. As for type of mulch, woodchips are great (unless you have slugs problems!) and I would stick to something like that for now, because (1) it's easy (2) living mulches take time to grow, and you can always plant them into your woodchips, and (3) they add nutrients to the ground over the long term. For a living ground cover, if strawberries (either cultivated or woodland) do well for you, they make a yummy groundcover that's easy to pull up if it invades your beds. I don't know if they can survive zone 3, though...
The bean/pea tipi should also be pretty easy/quick to set up, so you can probably get that made as you do the first garden bed.
After you get bed one and the tipi, I'd work on the next bed. I'm only really seeing 2 or 3 beds listed (child's garden bed, fun/varried garden bed, and forest garden bed). I'd just get the bed built and plant what needs to get planted at that time of the year in it, so if it's still spring, maybe the brassicas. If it's summer, get those squash in tehre. You can always refine the placements of the annuals the next year!
Moving the beds themselves year after year might be a pain. I'd set them up so that you can just rotate what grows in them. You might want to leave the children's garden as always the children's garden--that way the kids' have their own place that really feels like their own. My son has his own garden bed that we made last year, which he really loved. He grew all red plants in it. I know I made a thread on here somewhere...but I don't know where.... ah-ha!
Here it is!
I don't know if this helps, but I tried to make a thread about gardening with litte ones:
https://permies.com/t/69330/Tips-Tricks-Gardening-Wee. If there's any more tips you have, please feel free to add them!
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