DEET based repellents applied to the skin help. For added measure, wear light colored long sleeve pants tucked into your socks and long sleeve shirt. Light colors allow you to see ticks more easily than a dark colored garment would. In addition, pick up some permethrin garment spray (REPEL and Sawyer) are common brands sold at many outdoors/sporting goods stores like Academy and REI. The nice thing about permethrin spray is any bugs like fleas/ticks/mosquitos/horse or sandflies that land on your clothes will be killed. In addition, the spray has long residual activity and will last through several garment washings.
As for the lyme, you were smart to get checked out quickly. I'm surprised your FP sent you to the ER to get treated as diagnosis and treatment is fairly straight forward, but in any case now you know what it is/how it's contracted and what erythema migrans looks like. Lyme can be bad if left untreated, but Rocky Mountain Spotted Fever is worse and is also tick-borne. You definitely don't want any part of that because most clinicians will never see it and it's low on their radar screen, especially if you develop symptoms in areas where RMSF isn't routinely encountered.
It's OK to wheel with your kids, just take the same precautions with them. Educate them to never approach snakes or wild animals or venture near cliffs/ledges as well.
Also, anytime you come home after being in a tick-infested area, immediately strip down naked and closely examine yourself and kids for any ticks on your body...check skin folds, crotch, armpits, back of neck, etc. Many ticks are absolutely tiny when they haven't filled up on a blood meal, so look very closely. Also don't forget to check the scalp.