You can see your relations with all the parties in the library. If you want to avoid getting no-confidence voted you should try using one of the advisors that has the ability to improve relations with the coalition parties, it, unlike the card for improving relations which only does so for 1 party, improves relations with all the parties in your coalition. Having better relations with the coalition parties also means you can go for the compromise options when crises happen, and thus take less of a popularity hit if you want to maintain the coalition.