Well, I'm late to the party, and there's too much for me to know whether all of this has been said or not, but I thought I'd toss my 2 cents into the mix.......
I really don't think this is clearly a Fe/Fi issue. If the ISTP is indeed ISTP, and based upon the info in the OP and whatever else I happened to read following it, it seems the problem is one of poor Feeling judgment, period.
Let's remember what Feeling is - a rational reasoning that determines value. People with inferior use of Feeling generally assign value poorly, and it is often because they've allowed their emotions to taint their evaluations. People who use Feeling well, regardless of it being Fe or Fi, do not allow emotions to steer the wheel, but simply use them as signals to be analyzed.
People with poor Feeling, especially in situations they are right in the middle of, tend to regard insignificant things as much more important than they are and fail to note what is truly significant. In this situation, when I compare what seems to actually be the verifiable details with the descriptive words/phrasing used and accusations made by the ISTP, then I see someone who has painted a distorted picture of the truth because they've failed to measure the significance of the details of the matter properly, in proportion to the context and to each other.
The most significant points are brushed over, barely acknowledged, and degraded to a lesser importance than smaller points as they don't back the emotions of the ISTP. The ISTP feels (as in emotionally) a certain way, and that is dictating her Feeling-judgment. This is an extremely biased and unfair way to evaluate. It results in a person picking & choosing facts to emphasis or de-emphasis according to what suits their agenda, which is being run by emotion. This is what I see the ISTP doing in the OP - blowing certain things out of proportion & ignoring major positive developments within the family to justify her complaining & negative (emotional) feelings towards them.
Many of the negative comments are value judgments made without any clear facts to back them up, and sometimes in direct contradiction of other statements. Over and over the ISFP is called "filthy", but then there is a brief admission that she has improved in her cleanliness once given some instruction. That is then glossed over with an unfounded remark that it will not last....
ENFP-what I said: Um, yeah I remember you mentioning she did that back when she first moved in. Once you gave her a list of what needed to be done has she been better about cleaning?
ISTP: Well, yes, I guess, but it is only a matter of time before she slacks and let’s everything get messy again.
Significant points about the ISFP mom that have been conveniently ignored or downgraded by both the ISTP (& many in this thread):
1. Whenever the ISFP has been given direct advice or offered help directly, she has taken it & made the necessary changes. A neglectful, selfish, ungracious person does not act that way.
2. She has humbled herself to a humiliating state of accepting charity from people who resent her & her children, and yet, she has still put the welfare of her family over her pride in all these situations (except canceling the doctor's appointments).
3. The husband was responsive to the suggestions made by the INTJ. Any person may be defensive at first; that is a natural reaction. Real ingratitude is ignoring it all together. Again, the point seems brushed over that he has taken some of this advice to heart, as demonstrated by his actions.
The parents actually were fairly responsive to the INTJ-he talked quite a bit to the husband about financial responsibility and being responsible for taking care of a wife and his children. He said the response was defensive but it seemed to sink in some.
Are these the actions & attitudes of people who do not care, who are ungrateful, and/or who neglect their children?
After witnessing these changes, to then accuse (albeit, indirectly) the family of those "crimes" is distorted. The evidence shows otherwise, and it is nearly slanderous to imply those things. It is unfair to not recognize these improvements at their proper value, which is quite significant. These are all important indicators that the family is on the right track. To expect 100% perfection, immediate change overnight, etc, is unfair. Instead, they need to be gauged within the big picture, which shows more improvements than mere stagnation or even backsliding.
The accusations left are all questionable, as they have no solid evidence and mostly amount to speculation... The kids don't talk yet - or do they? The kids don't eat solid meals yet - or do they? We only know they don't do these things around the ISTP. Some of the accusations are too subjective in nature to take at face value - the ISTP thinks the kids run around like dogs, well, some people think its natural and acceptable for kids to be rambunctious as toddlers. Others expect children to be quiet and inconspicuous. Whose standards are being used? Is either morally incorrect or grounds for implying a parent does not care about her own children?
The problem with the ISTP's judgments is poor use of Feeling in general, not Fe vs. Fi, IMO.