Personally I think you are within your rights to remind another child of your or someone else's rights. So not to tell them what they have done is wrong, or tell them off... but let them know how they effected someone else.

In the case of the bike I would go up to the child and say "This is DS1's bike. We like people to ask before they borrow our bike. We would like it back now, thank you". I don't think your son needs to learning about "sharing" in that case as it's not sharing, it's stealing. I don't blame the Mum for not intervening- for all she knows you lent it to her son.

In the case of the play centre I would (and have) reminded older children that this play area is for children under 5. Then point them to the older play section. With the parent so close it makes things harder as they know the rules so they obviously don't care they are breaking them. Tricky.