When a possessive pronoun is not present it is assumed that the object/person belongs to the subject. In this case thus MY daughter.
English is obsessed with possessive pronouns. It makes sense because their presence allows you to omit an article. Czech, not so. If the daughter was somebody else's you would say so. Jane's daughter, etc. Or rather "Janina dcera".
Sentences like "he puts his hand on his heart" when translated word by word sound silly in Czech. We would be confused as to who else's hand but his would he be putting on who else's heart?
tee shirt is just another spelling of t-shirt.
We have a problem that there is no common Czech word for all the stuff that includes tee shirts, (dress) shirts, polo shirts and what not are still shirts in English. Košile is a (dress) shirt and nothing else, it has buttons all the way down and collars. Triko is a tee shirt and nothing else. Typically it has no buttons. Polokošile is a poloshirt. There is no common term for all of these and hence there is a problem whether the common English term should or should not be accepted for one of the Czech ones. I am more confident about the other direction, but here we may still require the specific translation.