I don't know much about pre-WWII Czechoslovak history, so I'll defer to somebody who does know, but I was under the impression that Czechs and Slovaks never really got along within Czechoslovakia (though that was probably more a result of the difference between the Austrian policy towards the Czechs and the Hungarian policy towards the Slovaks than any sort inability of the Czechs and Slovaks to get along).
Slovak support for Czechoslovakia came with knowledge of Slovak politicians, writers, lawyers and other engaged in Slovak national revival that Slovakia as such does not have enough educated people to run country by themselves.
There was simple reason for that. There were not Slovak High Schools in Slovakia from 1875 when last was closed by Hungarian authorities till 1918. Whoever studied at High Schools and Universities did it at Hungarians in Hungarian or left for Czech lands where they could study in Czech.
However later there were disputes about Slovak autonomy which was promised. However even supporters of autonomy as Andrej Hlinka and his People Party were supportive to Czechoslovak republic up to Munich.
Of course there was other reasons for disputes - for example to help Slovakia after A-H was dissolved huge amount of Czech professional came to Slovakia. From policemen and soldiers to teachers doctors, bank clarks, railway and post office workers.
However in 30-ties there started to be sufficient amount of Slovaks with education however unable to find work due to Great depression but also because work was taken by Czechs in Slovakia. Some numbers are saying something between 100-200 000 Czechs officials were working in Slovakia. Their help was very important for Slovakia but Prague didn't realize complications it can cause later.
In my opinion that's was one of biggest problems in Czech - Slovak relation at the time. Probably if they started to remove them slowly as young Slovaks started to come out from schools it would be better.
On other side cutting ties with Hungary caused problems for Slovak industry which was orientated towards Hungary and Balkan. That's was another problem. Different railways rates for deliveries from Slovakia to Czech lands and further which were not very favorable for Slovak based companies and I believe were based on old A-H rates didn't help either. I believe this issue was later addressed but already caused a lot of damage in Slovakia.
Slovak parties including Hlinka's People parties tried to address the problems and supported Czechoslovakia sometime more sometimes less when following their own agenda. However Czechoslovakia was seen as a wall against Hungarian revanchism. After all Slovaks on territories Hungary annexed after 1st Vienna in 1938 was could see what would be expected if Hungary took over whole Slovakia again - Slovak schools were closed, teachers expelled, Slovak students prosecuted or pressed to switch to Hungarian High Schools etc. Of course this had consequences after WWII when Czechoslovakia and Slovaks followed similar policy for at least a decade after war towards Hungarians.