New answer for the specific context:

You did your best with the 2 year old. Toddlers are difficult because they just make noises and expect you to work out what’s wrong for them. Small snack and something to drink are always good starting points, followed by a distraction (like the nursery rhymes video) to get their attention off what was upsetting them.

With the 5 year old, you escalated by increasing the punishment to 15 minutes, and now your brother-in-law pushed it back down she knows you can be overruled. Talk to your sister and her husband to make sure you’re both clear on what limits your comfortable with and what specific punishments to give for breaching them, in line with what they’d normally give, so you can both be sure you’re giving out punishments they feel are appropriate, so there’s no room for her to get you overruled - if she goes to her dad you should both be confident he will back you up. She’s of an age where she is going to test what rules and limitations really exist, so you need to make sure she’s not getting mixed messages about it. You’ll have an easier time distracting her with something interesting than telling her not to do stuff.

Make sure to use vocabulary they understand, but don’t be condescending with it. They’d rather you speak to them like they’re older than they are than younger.

Don’t be overly restrictive of their freedom, but be clear about the limits and make sure to enforce them. Explain the reasons for the restrictions rather than just telling them they’re not allowed and they’ll generally listen.

Give them small jobs to make them feel more responsible and patient about other things.

Do your best to answer their questions properly instead of dismissing them, even if the only answer you can give is “I don’t know”. They’ll listen to adults that they feel listen to them.

Some kids will test your boundaries. They don’t mean to upset you, they just want to be sure the rules are the rules. Just stay firm, keep repeating. I had to put the 2yo kid of a friend in ‘timeout’ (put in another room and briefly close the door, explaining why) because he was testing out my boundaries by throwing my stuff on the floor. This can get worse when they are tired, to the point where they want everything and nothing till they pass out - this particular toddler stood next to my bed, complaining about everything (especially the lack of mother’s milk!), not wanting to enter while I was just repeating my invitation to join me. In the end he fell asleep standing. No problem, I then lifted him onto the bed where he took his nap.

I think a lot of us still grew up in situations that were escalated into some kind of conflict by the grown ups around us, and we somehow carry the idea that when our kid doesn’t show the desired behavior we have to become louder, more threatening, come up with punishment … It’s not what I see working well in real life. As a grown up your job is to be the rock, the source of calm, the unbothered person, the voice of reason (I know, it’s so hard!). And repeat, repeat, repeat. The toddler will not understand immediately that throwing stuff is a bad idea, so you tell them, and tell them again, and again … but always keeping your cool. In a couple of years they will have grown out of being a gremlin, you know that and they don’t. The toddler phase is intense, seems to last forever, but is actually very short! I find it useful to explain everything in words even to very small children. They understand more words than they are able to say. Letting them know why they can’t have or do something shows respect and consideration and can avoid a screaming match.

Putting a toddler in bed and let them wake up with someone else is not an easy situation for them, it was probably a bit of a no-win. I know I’d freak out waking up in a strange house without my usual person!

Keep your promises and be predictable. Predictability and clear rules and consequences create a sense of security and it will make it easier for them to comply. Treat them with respect, they are small, not stupid. Treat them kindly but firmly, what they want isn’t always what they need.

You also might want to talk with the parents about this, they know their kids best and can give specific advice. What works with one kid, might not work with the other.

This is a wildly vague question, but a snippet of advice I was given years ago by a mate with a kid a few years older than my (then) toddlers was “You don’t have to provide them with constant entertainment, you just need to do one or two activities for a short amount of time and that’s what they remember”.

It’s great advice. Kids at early ages can be a fucking nightmare, but the truth is, you take them swimming for an hour, or do some painting for a while, or go to the park for a bit, and that’s what gets imbued on their consciousness. You get the rewards when they fill in that little book at school about what they did at the weekend, and it’s a ten minute window of shit you did that was fun for them, and not the rest of the stressful admin that comes with dealing with young children.

My nearly adult kids often say to me now “you were always doing fun things with us”. Mate, I played table tennis in a shed with you for 20 minutes, or sat down with you for a bit and made a robot out of a fucking cardboard box and a bog roll.

One or two activities a day where your attention is fully on them is enough to create happy memories for them. You don’t need to helicopter about.

Feed and water them regularly. Don’t let them die. If you can make them happy, that’s good too.

They just want to be a part of our lives. Involve them in your routines. Going grocery shopping might be a chore for you but it is a trip for them.

Always make them think it is their choice. If they don’t want to eat abc and xyz but the dinner is abc and xyz, ask them what do they want to eat first - abc or xyz?

When it’s almost time for them to switch from a preferred to a less/non-preferred activity, asking them “Do you wanna quit/start now, or in 5 minutes?” makes it feel like it’s their choice

They are information sponges. They won’t understand everything, but they will catch on to at least some things. Don’t treat them like idiots. Don’t be unfair. Don’t be arbitrary.

Because it’s fresh in mind from a personal conversation, e.g., if a parents treats one child better than the other, the other absolutely sees it and she will remember. Reactions may vary, but she sees it and will make future choices with that information in mind.

Avoid any situation in which you might have to do so.

Age really makes a difference in how someone might answer.

order pizza.

employ video games.

Pay attention to them even if you aren’t engaging with them - they can create all sorts of mayhem very quickly. My friend’s kid managed to lock himself in an operating washing machine. One of my kids managed to shave the center of his hair (to be like dad). And my other kid can find the most expensive item in a room and break it immediately (a true talent).

Sounds very general. How long are we talking? How old are the kids? How many?