I really hope to use this phrase when I visit the Czech Republic with my daughter :D
I submitted "That castle is my daughter's." "That's my daughter's castle" would be even more natural, although I didn't try it.
Be careful here. There is no difference in grammar or meaning between "That is my daughter's castle" and "That's my daughter's castle". On the other hand, "That castle is my daughter's" is a different sentence, both in English and in Czech.
Granted, the meanings are similar. But, both in English and in its Czech translation, the "that" in "that castle" is a demonstrative adjective, and in Czech must be modified to agree with the noun that immediately follows it (ten/ta/to/ty, etc.). In contrast, the "to" in the Czech sentence that means "that is/those are" is a demonstrative pronoun (not adjective) with a fixed form.
Will there be an explanation somewhere of how declension and plural forms work in combination? Do we know from the sentence "To je hrad mé dcery." If one or more daughters are being spoken about? In English if it were a single daughter it would be "That is my daughter's castle." and plural daughters it would be "That is my daughters' castle." I found this on Wikipedia but it's a little confusing, at least for me https://en.wikipedia.org/wiki/Czech_declension#Plural_forms
Dealing with cases in Slavic languages is hard if your mother tongue has the remnants of this concept only. The possession is signalled by the genitive case. Noun and possessive pronoun (and also adjective if it exists) denoting the "thing" possessed agree in the use of case. Here we have moje (or má) dcera (nom. sg.) - mojí (or mé) dcery (gen. sg.).
In the plural you can follow the same idea of genitive case, but the inflections are plural-specific. moje (or mé) dcery (nom. pl.) - mých dcer (gen. pl.)
So you can see that it is the 'y' in dcer
y (gen. sg.) which gives away the fact that this is about one daughter. The plural version genitive is very much different. Even when forms for different cases overlap there is usually some difference in the inflection left to disambiguate the meaning. I leave it to you to construct the plural version of the sentence now :)
mattvik, the explanation you seek is in the Tips and Notes for this lesson. Sort of. It's all in the tables. See the tables for Feminine noun endings and Possessive pronouns.