Have the original war fail. An alt-French Revolutionary war leads to some negotiated kind of peace(this is like OTL Republic of Ireland without partition). The British write up a constitution afterwards, where they are technically independent but the British control things like the navy and appoint people into this upper house. There is a second conflict in the 1820's, and this leads to independence, and a very different constitution is written(given slavery is on the wane and the brief period of semi-independence gave them a structure to build on).