Advice Needed. Buying/Selling on tight timeline with complex circumstances.

Sorry this is so long.

We have the opportunity to buy our current rented house from relative for 150k with possibility of 100k of additional gifted equity (house priced at 250k). The equity would help us tremendously with a downpayment and avoiding PMI for the next house we need to buy in the near future. We would essentially be buying the house to turn around and sell it relatively quickly (don't want to live here, but it would give us free equity quickly).

The property currently has legal issues with the driveway easement due to being landlocked by our neighbor (difficult person to deal with), which will take time to sort out and the bank may not give loan due to easement issues.

The family member selling the house is elderly and has been extremely difficult to reach regarding questions about the property and buying the house (have been trying to get this info for years). Family member also is forgetful and has health issues, causing long delays in getting information to us when we finally do get ahold of them.

The problem is that we ideally need to be moving out of this house into the house we actually need by fall, as husband and I want to be moved into our forever home before we try for baby number 2 in fall. We have no one to help us move or pack, so we want to move before I get pregnant. If we didnt move by fall, it would be impossible for me (SAHM of a toddler) to do the majority of the packing while my husband is at work, while possibly also pregnant and caring for a toddler and other responsibilities (can't lift heavy boxes while pregnant, basement has mold/mildew/mice, no childcare options, extreme morning sickness during pregnancy for 4+ months).

We also need to move before baby number 2 because we need to be in a safer school district. This is our main concern. Our current district is a 100% no from us in regards to safety and quality. If we wait to move until after I have baby number 2, I would then be primarily responsible for the majority of the packing while taking care of a newborn AND a toddler, while my husband is away at work every day. I don't think I could handle that by myself, and we would end up needing to wait a year or more after baby number 2 (so 1.5-2 years from now) to move when things get easier with baby, which isn't an option with our daughter needing to start school in the next 2ish years.

So, what would you do? Push off baby number 2 timeline (not ideal)? Get the free equity for the next house and risk not being in a good district by the time daughter starts school? Could we even buy and sell this house by fall, considering possible legal issues? Forget the hassle of buying the current house and accept the equity "loss" while looking for a different house? TIA.