If you live in a diocese that celebrates the Ascension on Thursday, but you're out of town and temporarily in a diocese that celebrates the Ascension on the following Sunday, what are you supposed to do? I know that for short trips you're supposed to follow your home diocese's rules, but in this case the diocese you're in won't have the Mass you're supposed to attend.
Obligation attaches to the day not the particular Mass text; e.g. if the priest opened the Missal to the wrong Mass, you still meet your obligation.
The canonist writing Canon Law Made Easy concludes that for Holy Days of Obligation you are bound based upon where you normally reside (known technically as having "domicile" or "quasi-domicile").
Thus, if you are obligated to attend Mass on a day but are currently in a diocese which does not observe Ascension, any Mass in a Catholic rite will suffice.
Naturally, this might mean an inability to attend Mass if, for example, all the parishes you could reasonably drive to did not have a scheduled Mass because it wasn't a Holy Day, fulfilling the obligation would be impeded, but you would not be culpable.
Canon 13 does specify that travelers are not bound to particular laws when absent from the territory unless "unless either the transgression of those laws causes harm in their own territory or the laws are personal"
It's hard to see how NOT going to Mass outside your territory would cause harm within the territory, so that doesn't apply, but there is a question whether the particular law establishing an obligation is personal or territorial.
There is some ambiguity around the obligation in this case. Technically, Holy Days of Obligation are created by Universal Law and then suppressed by a Bishop's Conference (Canon 1246), so most likely the suppression is a particular law, not the remaining obligation. Thus, Canon 13 about traveling wouldn't affect the obligation to attend on Ascension but only the suppression of that obligation elsewhere.
Ascension Mass when traveling between dioceses?
Generally speaking, the obligation is to observe the rules of the diocese you are physically and currently in at that moment. That is why, Catholics must be kept up to date of such things when traveling.
In the United States, Christmas Day (December 25) and the Immaculate Conception (December 8) are always days of obligation. Christmas and Easter (which always falls on Sunday) are the highest-ranking holy days, and the Immaculate Conception is the feast for the United States. However, if any of the other holy days falls on a Saturday or Monday, they aren’t considered holy days of obligation, because they’re back-to-back with Sunday. The concern is that it would be burdensome to many Catholics to have to go to church two days in a row.
To make things even more confusing, some parts of the United States have moved holy days, such as the Ascension from Thursday to the closest Sunday. If in doubt, it’s best to call the local Catholic parish or just go to Mass anyway. Attending Mass is never a waste of time, even if it ends up not being a holy day of obligation.
Europe has four more holy days than the United States observes: January 6 (Epiphany), March 19 (St. Joseph), Corpus Christi (Thursday after Trinity Sunday, which is the Sunday after Pentecost, which is 50 days after Easter), and the Solemnity of St. Peter and St. Paul (June 29). - Holy Days of Obligation in the Catholic Church
If a particular church within a certain diocese does celebrate the Feast of the Ascension on the Thursday (usually some religious communities) and the diocese transfers the feast to the following Sunday. Now let us say that some of the faithful go to mass on the following Sunday after Ascension Thursday and the they go to such a religious community’s Sunday mass which is not the Feast of the Ascension, their day of obligation has been fulfilled, even though they actually missed the liturgical feast of the Ascension. This actually happens every year in my archdiocese.
Canon Law makes this quite clear:
Can. 12 §1. Universal laws bind everywhere all those for whom they were issued.
§2. All who are actually present in a certain territory, however, are exempted from universal laws which are not in force in that territory.
§3. Laws established for a particular territory bind those for whom they were issued as well as those who have a domicile or quasi-domicile there and who at the same time are actually residing there, without prejudice to the prescript of can. 13.
Can. 13 §1. Particular laws are not presumed to be personal but territorial unless it is otherwise evident.
§2. Travellers are not bound:
1/ by the particular laws of their own territory as long as they are absent from it unless either the transgression of those laws causes harm in their own territory or the laws are personal;
2/ by the laws of the territory in which they are present, with the exception of those laws which provide for public order, which determine the formalities of acts, or which regard immovable goods located in the territory.
§3. Transients are bound by both universal and particular laws which are in force in the place where they are present.