It's ok to condition at home if you're only working out 2x a week, unless you can't recover from it. 2x a week really isn't enough training time, imo, to get strong. It's better than nothing but not as good as 4x a week or 2x training and 2 strength sessions.
Weights, what kind of weights?
For bars, I would focus on the:
pullup
hanging leg lifts besides v-ups, tuck ups, straddle-ups, single leg v-ups
pushups toward handstand pushups
hanging L
hanging straddle-L
and possibly hanging V-holds (in a hang, toes to bar with head in).
hollow holds or just hollow lifts. you make sequences like hollow hold for 5-10s, 3 v-ups, hold for 5-10, 3 more v-ups, etc
test your ability to do a pullup, chest to bar is better than chin over bar. I would prefer a hollow body when pulling versus an arched body or a body using a swing to pullup.
if you cannot perform a regular, dead hang pullup; try doing a pullup with the body horizontal or a jumping pullup, hold at the top with a slow descent
test your max number of pullups, cut the number in half and do 5 sets of these. same with pushups and leg lifts
if you cannot perform a leg lift to horizontal, work on doing them in a tuck to the chest.
before you do the pullups, pushups, and leg lifts, practice the L or V-hang and straddle-L hang about 5-10x. rest as necessary between holds, 30-60s. yeah, it'll take some time to get through this
another good type of leg lift is hanging leg lift toes to bar extend to candle/crade (straight inverted position) and lower down.
another is leg lift toes to bar, straddle through to inverted straddle-L
rocking levers is good. pull to flex arm hang, rock to candle/cradle. start these first in a tuck position and slowly over time and sessions extend to a straight body
skin the cats on the bars are a good exercise as well. L-hang pullups or wide arm pullups with an L-hang are tough as well.
try doing pushups with the bar under your chestbone or ribs instead of your shoulders over your hands.