"Inviting someone into someone else's home even once is pure entitlement. The daughter-in-law isn't taking advantage of anything because the op has agreed."
Lots of people agree to do things because they've felt pressured, or obligated - agreement doesn't necessarily mean that no advantage is being taken.
Given that some people are totally okay with this, and others aren't, I'd say that OP and her mil are just different types of personality on this issue, rather than mil being 'entitled'. Shes just in the camp who wouldn't see this as a problem. It's not helpful to look for offence where none was intended.
I wouldn't like having people in my house either, but if I've trusted my parent with my children, then I have to trust their judgement when caring for them. Sometimes we have to accept compromise and putting up with something we don't ideally want, because we are gaining more than we lose.
Obviously if mil was inviting people round who went through the OPs possessions and were disrespectful of her home, that would be one thing, but these are old family friends, who are known to the dh and are decent people.
It's a big thing to sit in someone else's house all day, minding their kids and to be completely unable to get on with any aspect of your own life at the same time. This just breaks up the boredom of the day a bit for mil.
As for the poster who would resent mil and friend using the expensive coffee pods - you do realise they cost about £5 per box and mil would need to go some before she got anywhere close to costing you what you are saving in childcare fees! The mind boggles at how short sighted some people can be. Weirdly, minding kids is not a total joy - not even the ones you love. Free childcare is a huge favour, so don't piss off parents/in-laws by moaning about them making themselves comfortable, while going you this huge favour!