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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
There is no harm on the person who has eaten garlic or onions to perform the prayers. He is only forbidden from going to the mosque (for the congregational prayer) until he gets rid of the smell of the garlic or onions (on account of the discomfort that his breath will cause for the angels and his fellow worshipers).
Since you pray at home, you bear no sin, and it is not disliked that you perform the prayers after having eaten garlic. However, if you try to remove the smell before praying in order to attain perfect Khushoo’ (humble submission and concentration), that would be better. Eating garlic is lawful, so if you wish, you can eat it, and if you wish, you can refrain from eating it.
Shaykh Muhammad ibn Ibraaheem wrote, “It is not prohibited to eat the vegetables with an unpleasant smell like onions, garlic, or leeks either because of craving them or for medication; they are pure and lawful for consumption. However, whoever eats such foods should not attend the congregational prayers, but he should not use eating them as an excuse to miss the congregational prayer and the Friday prayer (at the mosque). It is better to remove this unpleasant smell if possible.”
You are not obliged to obey your mother in eating garlic, and it is good to use any product to remove the odor of garlic from your hands and mouth.
Allah knows best.