You have a great attitude - enjoy the surprises. I agree that things sound close together but you can wait/watch. Thin by pulling out every other or at least the weaker of the two shoots. For tomatoes, cut off the "suckers" which are little branches off the sides that product no flowers. The flowers are where the fruit comes in and the other branches just take energy. Put a 2" high collar of cardboard around each plant (a few inches in diameter and both above the soil an inch into the soil about 1 inch - it stops cutworms from shearing off the new plant. You also need to support tomato plants - you can find tomato "cages" at garden centers and yard sales. They are worth it. For cucumbers in small space, try letting them grow upwards - use garden netting and some stakes, or even some old stakes/broomsticks and twine between them to make a grid - the vines' tendrils will grip and support the plants once they get started. The squash will need room to roam, depending on what you planted - butternut and those types will vine all along the lawn. Zucchini grows in one place but it's a huge plant, so thin things out and pick young squash as they are more tender and they can double in size after a good rain.
When you water, do it thoroughly and deep to encourage the roots to grow deep. Surface roots dry out quickly and the plants don't flourish. Once the plants are established with deeper roots, you won't need to water every day.
In MA, especially at the Cape where you are, you need to add compost or manure (deodorized, don't worry!) or organic fertilizer to enrich the soil. Since things are already planted, scratch the soil around the plant but not right up against the stem - sprinkle on some fertilizer or dig in some compost (but don't nick the roots), cover with regular soil, and water thoroughly.
For slugs, I've heard that you can use crumbled up eggshells at the edges of the garden - the sharp edges deter them. Just rinse them thoroughly so the animals don't want them. You can plant marigolds to deter rabbits or use a fine mesh fencing or chicken wire around the edges. You can also use the fencing as a vertical support for the cucumbers. I think garden centers also sell fox urine which deters a lot of things that consider the fox a predator. You have to reapply after the rain but urine is safe and actually sterile (at least I think so - human urine is). Just spray it around the edges on the ground but not actually on the plants. I think you can buy it online too. If the kids catch lady bugs, release them near the garden - they don't eat everything, but they eat some things. If you find a praying mantis, you're golden as far as bugs are concerned! There are traps for Japanese beetles too but some people think they lure your own beetles as well as those from all the neighbors. LOL
When the weather gets cooler in the fall and you have harvested a lot of your current crop, you can put lettuce in between the existing plants - as they die, the lettuce grows in their space and in the cooler weather and you get fall salads. Don't bother with lettuce now in the heat of July. Next spring, try radishes - the seeds are big enough for the kids to handle and they grow quickly in cool spring weather. It's often the first crop.
Have a great time!!