Q: Alternative to iDVD?

No.

Why is there no iDVD on my new Mac? How do I get it and how do I install it?

https://discussions.apple.com/docs/DOC-3673

To burn a DVD with iDVD from the latest version of iMovie, you have to export the movie using the Export button and select 480p as the size. Open iDVD and start a new project, then drag that exported movie file into the iDVD menu window, avoiding any drop zones you see.

If you are using El Capitan see this thread:

https://discussions.apple.com/thread/7251191

Are there any alternatives (competing products) that offer similar functionality to iDVD?

No.

I've tried several different alternatives sold on the Apple App Store.  None of them come anywhere near the power and ease-of-use of iDVD.   I also use the latest Toast 15 because it will burn Blu-rays as well as DVDs.  Toast 15  Would be my second choice.  However, Toast is lacking compared to the great menu systems you can easily create with iDVD. With iDVD, I can make DVDs almost equal to what Hollywood can do.  (With Toast 15 you can have simple menus but you cannot control where the chapters start on the timeline.  You can choose to have a chapter every 10 minutes etc.) 

If you just want to burn a simple DVD a program called, "Burn" is acceptable.

An additional consideration is the media you are burning on. Regular DVD-Rs use a dye type system that gives a shelf life of 5 to 10 years.  A newer type disk is called M-DISC. These are good for hundreds of years, and are causing a resurgence in optical media. ( I am in NO WAY affiliated with M-DISC, I am just a customer. )

Just in case that you, like me, hadn't heard of M-disks before, you may find this enlightening:

http://www.extremetech.com/computing/92286-m-disc-is-a-dvd-made-out-of-stone-tha t-lasts-1000-years

which does mention the obvious paradox that you may well have a playable DVD in 1000 years, but where to find a DVD player…..

which does mention the obvious paradox that you may well have a playable DVD in 1000 years, but where to find a DVD player…..

Every storage technology faces the same question.  M-DISC is unique because it provides options that didn’t exist before. The stability of the M-DISC allows people to migrate data at their own convenience. Every other data storage option (Hard Drives, Flash Drives, etc) forces a repetitive and expensive physical rotation of stored data—re-saving the data before it is lost. So, the question isn’t about whether or not a drive will be available a few centuries from now. It is really about not having to worry about your data integrity until YOU are ready to do something else with it.

Optical Discs have been around since the early 1980’s and you can still read that original CD-ROM on the latest Blu-ray drives. There are also billions of CD’s, DVD’s, and Blu-ray discs with songs, movies, and data on them that millions of people want to be able to use. Just as the continuing market for LPs (Long-playing vinyl records) maintains a now-obsolete technology that was invented in the 1930’s because there are a lot of people who still want it, optical disc drives will be available for a long time to come because of the extraordinary penetration of optical discs into the lives of billions of ordinary people all over the world.

The article that you linked to says M-DISC cost $7.  I buy them on Amazon for about $2.90 each.

I'm a former user of Taiyo Yuden DVD+R, I've completely switched to M-DISC DVDs and Blu-rays because of its long life span.  So far, I've burned about 200 with zero problems. Interestingly, M-DISC forces you to burn at 4X ONLY.   I tried a variety of burning applications including Apple's Disk Utilities, Toast and others. In all cases the burn "locks" to 4X.  I guess there must be a method by which the blank disc talks back to the software to burn the proper speed.