Thank you!
Actually, I think I found the answer myself: there is a space between two alleles, so actually the first way also includes the information about both alleles, it just prints them in 2 consecutive columns.
My plan was to create .bed, .bim and .fam from .ped and .map afterwards, and run DFAM: family-based association for disease traits. But now I think of it, there probably should be a way to create those files directly from .vcf.
UPD: --make_bed should do it
ped/map is a very outdated and generally poor and memory inefficient way to store data. Would reccomend using another format if you can.