A: Oh boy. I hear you, loud and clear. Just reading the description of your happy family made me feel tired and a bit stressed. It's a lot. You are not imagining it, and you are not just overreacting.
And yet, it all sounds pretty normal.
You are the parent of a 5-ish-year-old and a 3-year-old, and those are intense years. There is tremendous "emergent growth" happening. That means both of your children are at a developmental place where they are becoming true individuals. The 3-year-old loves his new body; for the most part, it does exactly what he wants. All the fine and gross motor skills are coming together, and his imagination is as creative as it will ever be. Jumping off the couch as a snowy owl? Yes. Superhero capes? Bring them on! Rules and routine and household needs, although making a preschooler feel safe, are not important to him. He wants to play.
Your kindergarten-age daughter is also in an interesting place, developmentally. Still loving play and creativity, the average 6-year-old is also on her way to thinking a bit more rationally. The 6-year-old may be able to take a moment and reconsider an issue or find patience to wait for something (say, a snack). I love 6-year-olds: They still believe in magic while also showing a hint of logic. This is all to say that the jumping around and make-believe loudness are normal. It is play.
To make this more interesting, you mention that your children are on the shy and sensitive side. If this is the case, they are likely doing what's needed to get through school (being extra-"good" and following all of the rules), or they may just be bright and happy children who are lucky enough to have teachers they love. I don't know, but unless there is anxiety underlying their rule-following, they sound like happy kids who thrive with rules.
If they are truly sensitive, what you will find are two children who may be a bit more immature or a bit more anxious or a bit more emotional than average. You mention loud voices, big emotions and big tears, but I don't know if that is beyond what is normal, when normal for these ages is: being loud, big, outsize emotions and lots of crying.
You have Spidey sense telling you that you may need more rules at home. Look into that intuition of yours.
Every family finds its rhythm. Some families are more boisterous, some are hushed. Some families allow jumping off furniture; some forbid it. Some parents love the hubbub of loud and happy children; some parents love the quietude of a family with more rules. But I will say this: After working with families for over 20 years, rarely do the parents and children's temperaments match completely. And one of the hardest combinations is the parent who loves peace and the children who love noise and action. To the parent, this feels like an assault, and when you say that your stress hormones are coursing through your body, you are not speaking in hyperbole; they are! Between the animals and the children and the noise and the jumping, your brain feels like you are being attacked.
You have to figure out how to bring more peace to this mayhem. Here are some ideas:
1. Get those animals crated or put away while you are trying to get things done. There must be a place for them to go, and I am sure that if you sat down and thought about it, you could find a way to make that happen. The animals may not like it, but so be it.
2. For meals, try to prepare as much as you can ahead of time. I know this is hard, but even a bit of planning on a Sunday evening will help. Stick to simple and nutritious. A time will come when you have time for lots of cooking. That time is not now.
3. Short of a tsunami, you have to get these children outside. Too cold? Get them to a kid's gym or a pool. Make them tired. Run them like puppies. (You know puppies destroy everything if you don't run them, right?) I am in no way saying that this is easy. But it is the lesser of two evils.
4. If you don't want the children jumping off the furniture, stop them. Now. In our house, you can jump on the basement couch, but not the living room couch. This meant, from the beginning, I had to scoop little kids off the couch and say, "No jumping off this couch." Over and over and over. And it worked (mostly). If you have been allowing all furniture to be used as playground equipment, you have a longer (but not impossible) path in front of you. You will need to find a place or time for them to jump (hello, children's indoor trampolines), and get ready to hold this rule with strength and compassion. Your children will agree to your new rules, turn around, and jump off the couch. They aren't liars or bad kids; they are just going back to bad habits. Get ready for more screaming and boundary-pushing, but know this will not last. Once they realize you mean business, your children will stop jumping on the couch.
5. Don't feel ashamed about getting help. From a mother's helper to an afternoon babysitter, there are so many ways to get a little help so you can have a breather and not feel panicked. There is nothing wrong with bringing in the teen down the street while you walk your dog. Or have the teen walk the dog while you play with the kids. There is nothing wrong with hiring a sitter one, two or five days a week. You are allowed to wave the white flag and say, "Help!" Will you need support like this forever? No. So allow yourself to solve this normal family problem with some temporary help.
6. Be sure to be keep a check on your anxiety and self-care routines. If you are proactive but still feel out of control, angry or overwhelmed, see your doctor and maybe consult a good therapist. What looks like "normal parenting exhaustion" can also be masking depression and anxiety. It is critical that you take a look at how well you are taking care of your emotional and physical needs.
Keep following your intuition. If it's telling you to tighten the reins on the rules, you may want to, but know that your children sound wonderfully happy and developmentally on target. Take good care of yourself, and good luck.