Some people are rather good at forcing the situation to go their way by ignoring the first, polite request and then trading on the fact that many people will not know how to push the issue without making it into a confrontation or sounding aggressive / argumentative in some way.
It definitely works as a strategy! As long as they have an extremely thick skin, and don’t mind doing that to other people. It works because so many people will just silently seethe or go into passive aggressive sniping, whilst the original person can just sail on getting their own way pretending to be oblivious to it all.
In order not to be swept along like this, you need to be assertive, and go further than a single request then fear of creating anger or hurt etc...
Reframing it as afresh way of doing things is a great idea. Then you have to stick to your guns. So smile, and repeat. Smile, and repeat. Then wait at the door or go ferret in the wash basket. You’ll only need to do this once or twice to show that you can’t give in on this one, and it’s just got to be this way.
If you just repeat your reasonable request, without any new bits on the sentence, just said again, nicely and politely. And then wait. And then they’ll be the ones to look awkward and unreasonable if they don’t just give you the ruddy clothes! It’s about nicely and politely throwing it back on to them, so you aren’t left feeling put upon and like you can’t say anything without being awkward and rude and creating a scene. But if you’ve said what needs to happen in a nice way, then stuck to it, there’s really not much they can do about it.
It will feel really difficult if you are not used to being assertive, and not taking on the role of being put upon and passive in the situation, but it really does work, and you’ll be surprised how easily it all falls into place once you start doing it!
If you’re faced with a real barrier to you picking up the clothes eg the machine is actually on with the clothes in it when you collect your child, then you need to come up with a solution that does NOT accept a return to the old behaviour. Eg you or dp going to collect the clothes the next day, even if it’s really inconvenient. This is important because otherwise all that’s happened is that you’ve made an effort to change behaviour and they’ve found a way to refuse and to continue to behave exactly as they are at the moment. You need to show that it’s just not going to be the same as before, and give no ‘mixed messages’ that your words are saying you need to change but you’ll accept their excuse to carry on just as they have before... Which will leave you resentful and closer to boiling point as you’ll feel they’ve done it on purpose to ‘win’, even if they didn’t even notice what they were doing!
In the interests in family harmony, being assertive is better than feeling put upon and quietly swallowing wrongs.