I am sorry that you have had such a difficult situation to deal with. Your dad is very lucky to have you and your husband.
For the VA's purposes the guardianship will not come into play until the initial claim has been filed and processed. You DO NOT want to address this issue at this point as it will only delay the processing of the application. Because he has dementia, which will be noted on the Physician's Statement, they are going to rule that he is incompetent to handle his own financial affairs.
The VA does not recognize POA or DPOA. They operate off of an antiquated fiduciary system. Providing your dad's application is approved, you would then address the issue of you being appointed as his fiduciary. What you do need to make certain of is that you include form 21-22a with your application assigning you as the "Claimant's Representative” You need to do this in order for the VA to speak with you regarding the application. Without it, they will not be willing to provide you any information ror the status of the application.
To the matter of you taking care of your dad in your home, you will need to keep records and show proof of where his income goes for your providing his care the same as you would if he were in an ALF or you had nursing staff coming in. Depending on his monthly income, you need to deduct out all allowable expenses including payments to you to determine his monthly "countable" income, which is the figure the VA will work with. I would suggest you visit this link to walk through the financial piece and have a better understanding of how to arrive at a proper amount.
http://www.vetassist.org/eligibility.htmYou also need to be aware that the VA requires an annual EVR to determine if his financial situation has changed primarily to confirm that he is still eligible and qualifies. Again, this is where keeping the records with a clear accounting of how his monthly income is spent will be critical. When they send an EVR you have a limited amount of time to respond. If you do not, they will stop the pension.
I hope that you will be successful with your application on his behalf and there is a ton of information on this site for you to learn from. My advice would be to take your time and make sure that the application is complete, that you keep a complete set of it for yourself, and that you send it Return Register Receipt to prove it was sent and received.
Come back as necessary, and keep in mind that everyone here is fighting the same battle for their loved one.
I'd like to make two requests.
1) Please take the time to share the site with those you know who may also be able to benefit
2) Please keep us posted with your progress. We thank you for your kind words and wish you the best!