Honestly, I didn't mind the majority of the songs in the sequels. Granted, there was always one or two every now and then that I absolutely despised, but for the most part I found them catchy and enjoyable. Some of my favorite songs in any kids movie are from the sequels also, for example "Always There," "No One Has to Be Alone," and "Bestest Friends" come to mind.
I can understand why Universal decided to go in this direction with the sequels. The Land Before Time is the kids franchise with the most installments in it, something it's major competition, Disney, did not have. In order to keep up with the competition, Universal had to try and do what they did, by going with a much more family friendly tone to their movies and add musical numbers. Now granted, Disney has had some VERY dark stories in their movies, but they are best known for their sense of family friendliness, if that makes any sense.
If any more sequels would be made, it would be guaranteed that musical numbers would be included, there's no getting around it. I would say tone it down to two or if possible just one. Normally there is always one song in every movie that sticks out and really sums up the message of the whole movie. Maybe keep just that one in and things won't be so bad.