My spouse's siblings keep stirring up trouble or interfering in our marriage. How can this be handled?

Let your spouse set the boundaries with their own siblings, and agree as a couple first; do not argue directly with the in-laws.
Allah commands verifying news before acting on it (al-Hujurat 49:6), and forbids tale-bearing and suspicion (49:12). The Prophet ﷺ said that a tale-bearer will not enter Paradise (Sahih al-Bukhari 6056). Practical steps: do not share marital problems with in-laws; when you hear a story, check it with your spouse; ask your spouse to tell their siblings that household matters are decided by the two of you; and keep polite family ties. If interference continues and does damage, reduce contact for a while and see a counsellor. See In-laws.