Accordingly, the meaning is:

When you rise for prayer, perform ablution, or bathe if you are in a state of major ritual impurity; and if you are ill or travelling, or have done something that more clearly entails ritual impurity—returned from relieving yourselves or had intercourse with women—

For the underlying wording is:

If you are ill or travelling and have risen for prayer, or, besides rising for prayer while ill or travelling, you have performed these two acts: relieving yourselves and having intercourse. Thus, your rising for prayer, illness, travel, and one of these two acts will have come together. Rising requires purification, while the excuse permits dry ablution; and this is the rising in question. Thus, when you rise, dry ablution becomes obligatory if it is merely rising, or if one of you has returned from relieving himself, or you have had intercourse with women.

Some people, however, take His words, “Or one of you has returned” and “Or you have had intercourse,” as coordinated with His words, “When you rise.” The underlying wording would then be: “When you rise, or one of you has returned, or you have had intercourse.” This, however, conflicts with the arrangement of the verse, which requires that this fall within the consequent of the conditional statement.

As for His words:

“If you are ill or on a journey, or one of you has returned from relieving himself, or you have had intercourse with women, and you find no water, then perform dry ablution,”

the interpretation just mentioned is close in meaning. The underlying wording, however, is:

If, when you rise for prayer, you are ill or on a journey, or if, in addition, one of you has returned from relieving himself or you have had intercourse with women.

Thus, it distinguishes between a circumstance on its own and a combination of circumstances. It means:

If you are ill or on a journey, rising for prayer merely by rising