Complex sentence: After learning that the general wouldn't be getting his inheritance Madame de Cominges leaves the hotel with her mother for Paris, taking Alexei with them after he wins big where he stays for a month and lets them spend his entire fortune on horses and frivolous balls.
Split into simpler sentences: After learning that the general wouldn't be getting his inheritance Madame de Cominges leaves the hotel with her mother for Paris. Alexei goes with them having won a significant amount and they stay together for a month, he allowing them to spend his entire fortune on horses and frivolous balls.