We found two work around for this. Both are just workaround and not the perfect fit solutions.

1. We provided link to URL A on home page and trained users to click on it when they log in so user is authenticated on both the URL and then issue does not show up.

The problem with solution one is its not automatic and user need to click on link to use our app which is very pathetic user experience.

2. We added home page component (of VF page type) on left panel which content a VF page from package. So when user loges in home page component load URL A and user is authenticated on both the URL and then issue does not show up. for better UI we can make the height of component as 1 or 0 to hide it.

The problem with solution 2) is, its automatic but user needs to wait till the component load completely. If user do not wait then it does not work properly.

We found two work around for this. Both are just workaround and not the perfect fit solutions.

1. We provided link to URL A on home page and trained users to click on it when they log in so user is authenticated on both the URL and then issue does not show up.

The problem with solution one is its not automatic and user need to click on link to use our app which is very pathetic user experience.

2. We added home page component (of VF page type) on left panel which content a VF page from package. So when user loges in home page component load URL A and user is authenticated on both the URL and then issue does not show up. for better UI we can make the height of component as 1 or 0 to hide it.

The problem with solution 2) is, its automatic but user needs to wait till the component load completely. If user do not wait then it does not work properly.

I have accepted this as an answer for now but if some one have better solution to this then please share it.