Ŝi dancas en ŝia ĉambro.

Does this 'necessarily' mean that one woman is dancing in 'another' woman's room?

Yes, absolutely. (But if you'll allow me to split hairs, the "ŝia" refers to a female, and not necessarily a fully-grown woman. That is, the "ĉambro" could hypothetically refer to the subject's four-year-old daughter.)

Otherwise, can it be interpreted in both ways?

No. The words "lia", "ŝia", and "ilia" never refer back to the subject, hence the reason for the existence of the word "sia". That is, the use of the word "sia(j)(n)" makes it clear that it's referring back to the subject. So if "ŝia" is used, it necessarily refers to someone different than the subject.

(Note that this does not apply to the words "mia", "via", and "nia". With those words, there is no confusion as to whose room we're talking about in the sentence "Mi dancas en mia ĉambro.")

There is one exception to what I stated above when I said that "lia/ŝia/ilia" never refers to the subject. it has to do with the fact that "si" and "sia" can never be used in/as a subject. So if you want to talk about someone and (for example) her brother, you would say:

• Ŝi kaj ŝia frato promenis hieraŭ. (She and her brother went for a walk yesterday.)

You might be tempted to say "Ŝi kaj sia frato promenis hieraŭ" as the use of "sia" makes it clear that you're talking about the subject's brother. However, this is wrong because "sia" is not supposed to be used as a subject, and that is why "ŝia" is used instead.

So that is the only time that "ŝia" can be interpreted both ways -- that is, as both her own brother and some other female's brother.

However, using "ŝi kaj ŝia frato" to refer to someone else's brother (and not the subject's brother) can be considered poor form, as it confuses who the "ŝi/she" words are referring to. It would be just as confusing as this sentence in English:

• She and her brother went for a walk.

if you meant "she" and "her" to refer to different female persons. If you really did intend for "she" and "her" to refer to different females, it's best just to specify who you mean instead of using "her/ŝia", in both English and Esperanto:

• She and Maria's brother went for a walk.
• Ŝi kaj la frato de Maria promenis.

Using two female pronouns ("she/ŝi" and "her/ŝia") so close together to refer to two different people is confusing in many languages -- and not just in English and Esperanto.

Ŝi dancas en ŝia ĉambro.

Does this 'necessarily' mean that one woman is dancing in 'another' woman's room?

Yes, absolutely. (But if you'll allow me to split hairs, the "ŝia" refers to a female, and not necessarily a fully-grown woman. That is, the "ĉambro" could hypothetically refer to the subject's four-year-old daughter.)

Otherwise, can it be interpreted in both ways?

No. The words "lia", "ŝia", and "ilia" never refer back to the subject, hence the reason for the existence of the word "sia". That is, the use of the word "sia(j)(n)" makes it clear that it's referring back to the subject. So if "ŝia" is used, it necessarily refers to someone different than the subject.

(Note that this does not apply to the words "mia", "via", and "nia". With those words, there is no confusion as to whose room we're talking about in the sentence "Mi dancas en mia ĉambro.")

There is one exception to what I stated above when I said that "lia/ŝia/ilia" never refers to the subject. It has to do with the fact that "si" and "sia" can never be used in/as a subject. So if you want to talk about someone and (for example) her brother, you would say:

• Ŝi kaj ŝia frato promenis hieraŭ. (She and her brother went for a walk yesterday.)

You might be tempted to say "Ŝi kaj sia frato promenis hieraŭ" as the use of "sia" makes it clear that you're talking about the subject's brother. However, this is wrong because "sia" is not supposed to be used as a subject, and that is why "ŝia" is used instead.

So that is the only time that "ŝia" can be interpreted both ways -- that is, as both her own brother and some other female's brother.

However, using "ŝi kaj ŝia frato" to refer to someone else's brother (and not the subject's brother) can be considered poor form, as it confuses who the "ŝi/she" words are referring to. It would be just as confusing as this sentence in English:

• She and her brother went for a walk.

if you meant "she" and "her" to refer to different female persons. If you really did intend for "she" and "her" to refer to different females, it's best just to specify who you mean instead of using "her/ŝia", in both English and Esperanto:

• She and Maria's brother went for a walk.
• Ŝi kaj la frato de Maria promenis.

Using two female pronouns ("she/ŝi" and "her/ŝia") so close together to refer to two different people is confusing in many languages -- and not just in English and Esperanto.