Is anyone familiar on filing a motion with the Veterans Affairs to become a trustee (because a family member is financially irresponsible)?

I want to tell you of my tale. My FIL, a Veteran, had to go to a nursing home. My wife and I paid his bills (rent and miscellaneous costs) while he was in the nursing home. Both the nursing home and VA claimed my wife and I were liable for bills before he was declared incompetent to handle his own finances. Sometimes the road to hell is paved with good intentions.

Think you're using the wrong terminology for the wrong thing. Typically there is a probate court application for incompetency in which when filed, also has an application for court appointed guardian. Trustees manage actual trusts, not people's lives. Guardians make all the living, money, medical, etc. decisions because the individual has been deemed not to be able to properly make those decisions on their own. If financial is the primary focus, then you file for a conservatorship and become a conservator. Once that is done, then you file with the VA to assume control over the relevant things. There's been some horror stories over the past few years in which VA was passing this stuff to BATF who would then send agents to confiscate the owners firearms. So it's important to know what it fully means to be a guardian or conservator. A probate lawyer is essential for you in figuring it all out.

Probably need to check at the local VA office for what you're asking.