It needs a LOT of very expensive repairs. Off the top of my head: structural issues under the kitchen floor, kitchen floor after water damage and structural sagging, every single window needs replacing, basement needs to repaired (everything ripped out and replaced) after sewer flooding years ago. And of course every major appliance is 15+ years old and on its last legs. (Furnace, water heater, washer/dryer, AC)
It's a much bigger house than we'd normally shop for. It's 5 bedrooms and comes with insane utility costs because it's so poorly insulated. We hope to have 4kids, but only have 2 right now so it seems insanely huge.
However, it's in an extremely desirable neighborhood with some of the very best schools in the nation.
In terms of how long we'd feel obligated to stay, I dont really know. We definitely couldn't just turn right around and sell it immediately, but we wouldn't necessarily have to stay forever.
The mother is a hoarder and all her things are in the house, even though she currently lives elsewhere. It would be a very tricky subject to even broach with her, much less the actual act of clearing things out, if we even got that far. Our family of 4 only has access to 1 bedroom out of the 5, if that gives any idea of how full the house is :)
First off, I've got two parents that were/are hoarders, so I am speaking from my experience here. No way in hell would I want to purchase a hoarder house since they always end up with extensive neglect and maintenance/structural issues, but then again, I would not choose to live with another person's things in my living areas at all. This is crazypants to me. So no, the house sounds like a horrible, terrible thing and I can't imagine why you're living there at all, much less even entertaining the idea of purchasing it.
Are you currently paying rent? Because I'd not be willing to do that with the limited access/living with hoarder stuff and horrible structural/cosmetic issues you describe. You have 2 kids and only have one bedroom actually usable? That's awful. And if you don't like the house and don't want to make all of those repairs, there's your answer. Get out now, find a great apartment or house in the general area and leave the parents to clean that mess up since they made it.
Do you really like the house and feel competent to take on all the repairs and upkeep it will require? Then I'd offer a ridiculously low offer on the house to buy it out from the mother. Of course, this is if the offer for the father to gift the other half to you stands, but be aware that you need to check int taxes or other complications - I know you need to live in the house a minimum of two years before selling to avoid the cap gains tax hit (like if the parents purchased the house at $100K, and it's now worth $400K, you'd be assessed $300K worth of cap gains if you tried to sell before living there 2 years - ouch).
So say the house would be worth $400K if it was in decent shape. You get a realtor out to run comps and an independent inspector to give you the breakdown on all the things that need to be fixed or updated to make the house match the rest of the neighborhood. Ballpark the repair costs.
Your dad gifts his half to you, and you offer the mom say $70K since it's going to take a ton of money to fix the things that need fixing and update the house to not be a scary nightmare place, as mostly it would be flippers that would expect to underbid to that level on that house anyway. I would make sure to have a complete inspection and estimates carefully listed out and noted for her so she sees that the house is really not sellable to anyone without these things fixed, and how much it will cost so she understands she is not going to get anywhere near what she thinks it might be worth and just tell her that's what you'd be able to afford since the repairs would be so extensive. She is welcome to consult a realtor if she thinks the house comps might be off.
Side note: Why if the parents are divorced do they still own the property? They should have either hashed out who keeps the house (one person should have bought out the other) or they should have sold it when divorcing. Your father can probably force the sale of the house if you don't want it since he should not be made to share joint property with an ex at this point (there's all kinds of liability issues when spouses/exes are still tied together like this). I'd suggest he consult an lawyer to untangle himself from his ex-wife at the minimum if you don't plan to purchase the house.
And finally, about dealing with the hoarder crap stored in the house. If you do purchase it, then give her until the closing to make arrangements to remove all of her property. It should be written into the purchase agreement that any property left in the house after closing is the new owners' property and you can use/dispose of it as you wish. If she wants to keep it, then she comes and gets it; it really is that simple. And if she gets angry, then let her; you are an adult and can tell her that she's had plenty of notice, and it's unfair to expect you to act as her personal warehouse - there are tons of storage units out there if her current house is too crowded. But you should not let her sickness hold your own space hostage. She can't ground you or take away your television privileges anymore, so if she gets angry, let her. And leave or hang up the phone if she won't stop harassing you over it - distance is sometimes a needed and necessary thing to enforce proper boundaries. It is healthy to have boundaries when dealing with your parents as an adult; do not be afraid to stand up for yourself and your spouse/children and don't be manipulated or guilted into doing things you don't want to do or putting up with crazy-making behavior just because they are faaaaaamily.