I would just plainly tell your H that his you need his help in upkeeping the house and meeting with agents. Just tell him, you can't possibly do it all yourself (timewise and moneywise). If he complains, just say "this sin't easy for me either, but if we want to have any prayer in selling this house we need to be able to present it well.
Perhaps the time spent "fixing" the house up could give you two some time togeher and bring out some good memories. I probably wouldn't discuss the split of funds or the cat right away, this will most certainly result in some sort of tension. Where I am at it usually takes a month to complete the transaction so this would give you plenety of time to work out those details. This is just my perspective others might prefer to get those details straightened out ahead of time.
TwinDad Me 39, W 36, M 11 W - MLC, WAW???? 2 Kids B/G 3 YRS Old Start of the Long and Bumpy Road..... On the verge of piecing.....a new beginning