What are the sources, even those that are rejected in the final halachic analysis, that encourage or allow a husband to physically abuse his wife?
In some cases (and this is accepted AFAIK in the final halachic analysis) a husband is not only allowed to beat his wife, but he must do so even to the point where she might die. An example of such a case is where the wife is attempting to kill someone else and this is the only way for the husband to stop her (see Rambam Positive Commandment #247). In fact there is even a special prohibition that he should not have compassion upon her in these types of cases (Rambam Negative Commandment #293).
source that the husband can beat her through bais din
if you are looking for him hitting himself see @Double AA's answer
כָּל אִשָּׁה שֶׁתִּמָּנַע מִלַּעֲשׂוֹת מְלָאכָה מִן הַמְּלָאכוֹת שְׁהִיא חַיֶּבֶת לַעֲשׂוֹתָן--כּוֹפִין אוֹתָהּ וְעוֹשָׂה, וְאַפִלּוּ בַּשּׁוֹט. טָעַן הוּא שְׁאֵינָהּ עוֹשָׂה, וְהִיא אוֹמֶרֶת שְׁאֵינִי נִמְנַעַת מִלַּעֲשׂוֹת--מוֹשִׁיבִין אִשָּׁה בֵּינֵיהֶן אוֹ שְׁכֵנִים; וְדָבָר זֶה, כְּמוֹ שֶׁיִּרְאֶה הַדַּיּן שֶׁאִפְשָׁר בַּדָּבָר.
כל אשה שתמנע וכו': כתב הראב"ד ז"ל מעולם לא שמעתי יסור שוטים לנשים אלא שממעט לה צרכיה ומזונותיה עד שתכנע עכ"ל:
Whenever a woman refrains from performing any of the tasks that she is obligated to perform, she may be compelled to do so, even with a rod. When a husband complains that [his wife] does not perform [her required tasks], and [the wife] claims that she does, [the dispute should be clarified by having] a [neutral] woman dwell with them or [by asking] the neighbors. The judges should clarify the matter in the best way they see fit.
Rav Kapach emphasizes that the Rambam's intent is not that the husband should beat his wife himself, but that he should bring her to the court, which should administer corporal punishment if they see fit.
The Ra'avad objects to this ruling, explaining that it is unheard of to compel a woman by corporal punishment. Instead, her support should be cut back until she accepts her household duties. The Rashba offers other options - to place her under a ban of ostracism or to sell her ketubah and use the proceeds to hire a maid.
When quoting this law, the Shulchan Aruch (Even HaEzer 80:15) mentions that the woman is compelled to perform her tasks, but omits reference to the means of compulsion employed. The Ramah quotes the opinion of the Rambam together with that of the Ra'avad and the Rashba, but appears to favor the latter views.
ps i do not like the wording of your question
if the torah "encourages" or "allows" something it is not abuse (it is proper)
Abuse is the improper usage or treatment of an entity
even-though now it is considered commonsense that the use of physical force is abuse
we still have laws that have to old point of view
A parent, guardian or other person entrusted with the care and supervision of a person under the age of twenty-one or an incompetent person, and a teacher or other person entrusted with the care and supervision of a person under the age of twenty-one for a special purpose, may use physical force, but not deadly physical force, upon such person when and to the extent that he reasonably believes it necessary to maintain discipline or to promote the welfare of such person.
pps a master can beat his slave
...שֶׁעַבְדּוֹ, יֵשׁ לוֹ רְשׁוּת לְהַכּוֹתוֹ...
...With regard to one's own (Canaanite) servant, one has the right to strike him...
but see the end of hilchas avodim
It is permissible to have a Canaanite slave perform excruciating labor. Although this is the law, the attribute of piety and the way of wisdom is for a person to be merciful and to pursue justice, not to make his slaves carry a heavy yoke, nor cause them distress. He should allow them to partake of all the food and drink he serves. This was the practice of the Sages of the first generations who would give their slaves from every dish of which they themselves would partake. And they would provide food for their animals and slaves before partaking of their own meals. And so, it is written Psalms 123:2: "As the eyes of slaves to their master's hand, and like the eyes of a maid-servant to her mistress' hand, so are our eyes to God."
Similarly, we should not embarrass a slave by our deeds or with words, for the Torah prescribed that they perform service, not that they be humiliated. Nor should one shout or vent anger upon them extensively. Instead, one should speak to them gently, and listen to their claims. This is explicitly stated with regard to the positive paths of Job for which he was praised Job 31:13, 15: "Have I ever shunned justice for my slave and maid-servant when they quarreled with me.... Did not He who made me in the belly make him? Was it not the One who prepared us in the womb?"
Cruelty and arrogance are found only among idol-worshipping gentiles. By contrast, the descendants of Abraham our patriarch, i.e., the Jews whom the Holy One, blessed be He, granted the goodness of the Torah and commanded to observe righteous statutes and judgments, are merciful to all.
And similarly, with regard to the attributes of the Holy One, blessed be He, which He commanded us to emulate, it is written Psalms 145:9: "His mercies are upon all of His works." And whoever shows mercy to others will have mercy shown to him, as implied by Deuteronomy 13:18: "He will show you mercy, and be merciful upon you and multiply you."
Blessed be God who grants assistance.