When applying for guardianship do the courts recognize the oldest child if one of the parents has passed away and the other parent is incompetent?

"Recognize" as in give special consideration to? I don't think so. Their guiding principle is what is best for incompetent person?

Something to keep in mind that if family is having infighting as to each of them wanting to be named guardian...... is that the judge does NOT need to appoint a family member to be guardian. Judge can appoint guardianship to others, like an attorney specializing in guardianships or someone else from a list of potential guardians that is already vetted by the courts.

The procedure I just went through was that I petitioned to be the guardian for my wife and all of her close relatives had to be notified of this. This is to give each a chance to object to me being her guardian.
If any objected it got a little more complicated. Either way, approval or objection by a relative, would be weighted by the court.
The court could approve the petitioner with restrictions that came from objections or on its own.
In my case it involved restrictions on withdrawals from wife's savings account.
It also followed the state guidelines favoring a spouse or family.
Note that things may be different in your area.
The court probably would not look too much at the age thing. It will normally look at only those that have petitioned for the guardianship.
Just keep in mind that if a court decides a petitioner is does or any family member does not measure up, it can appoint an outside person to the guardianship.
I hope this helps and good luck.