Yes you did not do your homework before having surgery. Read this carefully http://www.medhelp.org/user_journals/show/1648102/Consider-ALL-the-Options-Before-Your-Cataract-Surgery-Working-Through-Whats-Best-For-You Also
use the archives and search feature and scroll through the discussions over the past week. This situation has been discussed at length. Note especially the detailed discussions of Soft Ware Developer.
You have several options. You might want to post-pone the other eye until you understand what they are. Since you are happy with your distance (that means 20 feet and further away). You could opt to have the second eye done leaving you about -1.50 that would be called mini-monofocal distance bias. you could opt to have the second eye -2.50 that would be full monofocal. You might want to look into having a multifocal IOL or accommodating IOL put in the other eye. If toric multifocal not available now residual astigmatism can usually be taken care of by post surgery lasik or you might have femtosecond laser at the time of the second surgery. It will take you some time to consider all the options. there is no best option there are a number of options that are different for different people.
If I decide that a different lens is best suitable, can I replace the lens that was already paved in my right eye, if I act fast?
I would suggest you get an independent second opinion before you do that. There are other people that have posted problems like yours that replaced the IOL and were even less happy. If you make your near vision better you're going to make your distance vision worse.
I thought that is the purpose of a multimodal iol? Am I understanding it wrong?
Use the search feature and archives. This website is full of people that have had multifocal IOLs put in and are extremely unhappy with them: some problems: still need glasses for many things, poor night vision, waxy vision, dysphotopsia (unwanted light reflexes), difficulty with eyes working together. There are many postings of people removing multifocal IOLs and putting in monofocal IOLs. You have as you said very good distance vision that you will lose if you put in multifocal IOL. Explore making adjustments for near and intermediate vision on the unoperated eye.
It is unfortunate that they suggested clear lens replacement at your age, usually that isn't suggested until people are dealing with presbyopia and are already familiar with the issue of problems with near vision. If they suggest inserting a lens in the eye of someone younger, usually they don't remove the natural lens but instead its usually whats called a phakic IOL or ICL (which has its own risks, like the potential to cause cataracts).
There are premium lens options that you can have implanted in the US. However due to the FDA's slow approval process, there are more IOL options available outside the US like trifocals and the new extended depth of focus Symfony lens. I traveled to Europe to get the Symfony in Dec. 2014, but its now approved in Canada and Mexico. Someone recently posted about getting it at a clinic in Mexico within walking distance of the San Diego border with a prominent surgeon.
Unfortunately there is no perfect IOL, as the doctor's writings note there are risks involved with premium lenses, like the risk of problematic halos from a multifocal (though the newer multifocals have a much lower risk of that than older ones, and the "extended depth of focus" Symfony has risks more comparable to a monofocal). However the vast majority of people are happy with each of the various premium lens options. Those who post online are usually the unhappy minority, which merely serve as a reminder that there are some risks. There is a tiny chance you'd be unhappy if you switch and want to switch back to a monofocal, so its important to take the risks into account. However unlike the typical cataract patient who is in their mid 70s, those of us who will be living with IOLs for a few decades need to consider whether taking some risk is worth doing for the possibility of better vision for decades.
Usually I gather that lens exchange is an option at any point in the future as long as the initial surgery went well, though I've seen some mention that there are advantages with doing it soon, I hadn't researched how soon or what they are. Usually the only concern is whether the initial surgery damaged the capsular bag, or if someone has had a YAG treatment for PCO which can damage the capsular bag. Most premium IOLs are inserted into the capsular bag and can't be placed outside it, though there are some multifocal options that can be used outside the bag.