Older toddlers will be establishing bonds with a wider circle of caregivers but they will still look to their primary caregivers to provide a sense of security. They will also, at this stage, be developing their hand-eye coordination, language and thinking skills. Remember, though, that this period isn't called the 'terrible twos' for nothing and children at this age will readily throw tantrums.
A pattern of two non-consecutive nights a week with the parent who is not providing the main day-to-day care, plus one weekend every other week might work well. Try to limit the tantrums by making hand overs as quick and business like as possible and try to keep things like bed times the same in both houses. Strict routines will work for everyone.