Why should not we touch Tulsi and Peepal trees on Sunday?
As far as the Peepal Tree (aśvattha) is considered, not only on Sundays, but it shouldn't be touched on any other day except on Saturdays.
This prescription follows from the Skanda Mahā-Purāṇa 2.4.3.48
Chapter 3, Kārttikamāsa-māhātmya, Vaiṣṇava-khaṇḍa, Skanda-purāṇa
अश्वत्थपूजा स्पर्शेन कर्त्तव्या शनिवासरे । अन्यवारेऽश्वत्थसंगाद्दरिद्रो जायते नरः ॥ ४८ ॥
The worship of Aśvattha should be conducted on Saturdays by touching it. On other days if a man touches it he will become poor.