My parents will very likely need LTC in a few years as well and I have promised myself NOT to be the primary caregiver. I love my parents dearly, but I saw what it did to my mum when she was caring for her mother (my grandmother) who had dementia for a few years. It was terrible on my mother (and on me and my sibling too). It is emotionally draining to see someone you love getting worse on a daily basis, slowly slipping away and sometimes saying terribly hurtful things, not recognizing anyone etc. Physically it is also very draining. Cleaning your own parent after they soiled themselves...lifting them on and off the toilet...I don't want to get more graphic here, but it can get very very bad. If you are caring for a stranger, you can somewhat detach yourself mentally from it as one of my friend's who works in a nursing home explained. But if it's your own parent, you can't. You have it 24/7 and I know those years were the most terrible years for my mother. When it comes to this point, then I will not put myself through that. I will make use of every government program out there and I will spend my own money if necessary, but I will not care for them myself if they get to such a state. I applaud people who do it, but personally, I know I can't do it and I wouldn't want to put my own family through it.
Personally, I am not buying LTC insurance for my parents or myself. I have studied those policies quite closely and the premiums are very high and the conditions for actually paying out are quite strict. In my parents' case, they have zero assets, savings or income, so the government will pay for some of their care. I just hope that they won't need it too long if they should reach such a point. As for myself, pretty much same strategy. My stache should last for quite some time and if my old age slowly dying body finishes it off before I kick the bucket, so be it. I want to live a good life while it's good...it's impossible to plan for everything.
As to the OP, definitely look into any government funded programs and only use your own money when absolutely necessary. Put yourself first would be my honest advice. If I think about how I would feel if I was old and - inevitably - dying, then for sure I wouldn't want my children to deplete their savings. I know my parents wouldn't want me to do that either. If there are government programs that you can take advantage of, then do it. Get someone (even maybe pay someone) who can help you in this process, I know the bureaucrazy of this can be daunting. I am sorry you are going through this, make sure you take good care of yourself as well.
Also, make sure to get a DNR (do not resusciatate) for your mother (not sure how this works if she is mentally not capable to sign this herself anymore). Thankfully my grandfather did this in good time...otherwise a hospital may be obligated to preserve life...which can drag out the inevitable for years (as was the case with my friend's grandmother).