What should I do to remove the burden I feel during prayer, with the exception of prostration (sujud) and the prayer of waking (salat al-istiqadh), as I find comfort in them?

The heaviness you feel in prayer or the mosque is either from the whisperings of Satan or from the heart's attachment to worldly matters. The cure for this is to recall the virtues of prayer and staying in the mosque, to remember that you are conversing with your Lord, to repel evil whisperings, to wholeheartedly devote yourself to prayer, and to strive to attain khushu' (devotional humility). For whoever approaches it with sincerity, prayer dispels worries and removes sorrows. The Prophet, peace and blessings be upon him, whenever he was afflicted by a matter, he would pray. You will not attain the sweetness of acts of obedience except through struggle and perseverance. So strive against yourself until you find the sweetness of worship.