When things start getting hectic it's time to go do something. Get out of the house even if it's just to drive around the neighborhood a few times. Going to the park, to the indoor playground at McDonald's, walking through a mall, it's something to occupy the mind and get it on to another topic.
Kids don't need a lot of structure. In child care a typical day for a 3 or a 5 year old goes something like this:
7am-8:30am arrive and eat breakfast,
After eating to to classroom play
9am Circle time, days of the weeke, the outside weather, music, story time, monthly theme, weekly goals, letters, colors, etc....
9:45 bathroom time
10am play time
10:45 clean up and wash up for lunch
11am lunch
noon clean up from lunch and transitional activities such as reading a story or other quiet, sit down and relax type of things.
12:30 all kids asleep
2:30 start getting kids up and to the bathroom
3pm, after noon snacks.
3:30pm playtime until parents come or do some arts and crafts then play time.
So, as you see, a 3 year old needs to have play time most of the day. That's how they learn at this age. They don't need structure and a tight schedule. They learn by playing until they are a good 4 years old. That's why developmental research says kids are ready for the structure of an actual classroom at age 5. That's why kindergarten is for kids a full 5 years old turning 6 that year.
I suggest your child needs to learn to play on their own and not be using you as their playmate if that's what is happening.
Please google children learn while they play so you can see why child care centers have changed so much over the past 20 years. Kids learn all sorts of needed things by simply playing.