'p' in query #2 will, in general, correspond to a superset of 'm' in query #1. If that is your intention, then the following should work. Notice that the 2 MATCH statements have no common variables, but a WITH is required by the Cypher syntax, so I arbitrarily picked the variable 'm' to pass to the second MATCH (even though it will be ignored).
MATCH (n)-[r:RELATIONSHIP*1..3]->(m)
SET m:LABEL
WITH m
MATCH (p:LABEL)-[r2:RELATIONSHIP]->(q:OTHERLABEL)
WHERE r2.time<100
RETURN p,r2,q;
If you intend 'm' and ''p' to be the exactly the same, then just replace '(p:LABEL)' with '(m)':
MATCH (n)-[r:RELATIONSHIP*1..3]->(m)
SET m:LABEL
WITH m
MATCH (m)-[r2:RELATIONSHIP]->(q:OTHERLABEL)
WHERE r2.time<100
RETURN m,r2,q;