All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Among one of the rules of Sharee'ah is that hardship brings about ease, as Allah says (what means): {…and has not placed upon you in the religion any difficulty.} [Quran 22:78]
Allah also says (what means): {… Allah intends for you ease and does not intend for you hardship.} [Quran 2:185]
So hardship is waived from us, and based on this, if using water is harmful to your sister even when wiping on the hands and the feet instead of washing, then she may resort to Tayammum instead.
Shaykh Ibn 'Uthaymeen said (when talking about performing Wudhoo'):
"The scholars said: 'The wound and the like, is either exposed or covered. If it is exposed, it is obligatory to wash it with water. If this is difficult, then one wipes over it (with wet hands). If again it is difficult to wipe over it, then one should perform Tayammum; the method of Wudhoo' should go according to this sequence. If the wound is covered with any suitable cover, then one can only wipe over it. If wiping over it is harmful even though it is covered, then one resorts to Tayammum, as if it were exposed. This is what the scholars of Fiqh mentioned regarding this matter.'" [End of quote]
As for the issue of removing the socks after wiping over them, then this does not invalidate ablution according to the view of some scholars. But if she takes them off, she may not wear them again and wipe over them until she performs ablution.
Shaykh Ibn 'Uthaymeen said:
"If a person removes his socks after having wiped over them, then wiping over them again is void, meaning that he may not wear them and wipe over them again, unless he performs a complete ablution whereby he washes his feet. As regards him being in a state of purity if he removes the socks, then the purity remains valid and it is not invalidated by the removal of the socks over which he had wiped. If one wipes over the socks [after having performed a complete ablution whereby he washed his feet] then his purity is complete based on Sharee'ah evidence. Hence, such purity is not invalidated except by (another) evidence. However, there is no Sharee'ah evidence stating that removing whatever one had wiped over [whether socks or anything else] invalidates ablution." [End of quote]
Allah knows best.