Dear Noelia,
In general one would not add "rest" to the second level. Rather, one would set up differential contrasts on single-subject level, contrasting the conditions to the rest condition with e.g. [0.5 0 0 0 -0.5 ... 0.5 0 0 0 -0.5 ...] (averaged across the two sessions), and forward these con images into second level.
In your case, if it's really just either cond1-4 or rest, you might also just leave the "rest" periods unmodelled.
Concerning your actual question, this might well depend on the settings (variance, independence) of the two models and the way the contrast vectors were generated (maybe you accidentally took estimates from just one run for one of the models). It's difficult to guess without the details. In general, the Flexible factorial should be okay to look at main effect condition (within-subject effect) and the interaction, but for main effect group (between-subject effect) you should turn to Full factorial with a single factor "group", with the contrast images reflecting the average activation, that is [1/8 1/8 1/8 1/8 -1/2 ... 1/8 1/8 1/8 1/8 -1/2 ...] when modelling rest (or just [1/8 1/8 1/8 1/8 ... 1/8 1/8 1/8 1/8 ...] in case you leave it unmodelled). Alternatively you might want to turn to GLM flex for second level statistics, which uses partioned error terms resulting in valid results for any of the mentioned contrasts.
However, if your main research question is really just (cond1+cond2)/2 vs. rest for G2 vs. G3, I would simply build the corresponding contrast on single-subject level and forward this into a two-sample t-test on second level to test for [1 -1] and [-1 1]. But probably it's just one of several hypotheses you want to test?
Best,
Helmut
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