1) затягивать in this context - drag into, i.e. they get stuck in a situation, they get accustomed to it (затягивать may suggest the association with a quogmire, one is stuck and it's not easy to change it)
2) тянуть с заключением повторного брака = procrastinate (delay) with getting married once again... заключение - here official word meaning 'commission, taking into effect'.