The way the passage read it implied that Sir Walter Stewart was at that time with the Scots Army in the north with the King opposing Cromwell. It did not imply that they were cousins - he only referred that he had an ancestor by the name of Stewart. There was even the slightest hint that there was any Caldwell connection. The Western Alliance troops in Ayrshire were torn by sympathy for Cromwell (from a religious point of view)on the one hand and the natural loyalty to Scotland as he was an invader and an enemy. The Scots army of the North with the King were very distrustful of the leaders of the Western Alliance and were making moves to replace its leaders when they made an unsuccessful pre-emptive attack on Cromwell (to "prove their loyalty"?). Cromwell knew of their vacillation and went to great lengths to try and win them over to his side. Presumably after Worcester there was less need to dither and they threw in their lot with the Cromwellian government.
The Caldwell family comes from the area of the Western Alliance and are known to have been favourable to the feelings of that area.