ServantofMary -
The answers you get on here are going to be from one end of the spectrum to the other. Most who consider themselves “Traditional” Catholics will normally advise not to go (for all the reasons you mentioned you are concerned about, plus others). Those that fall in the conservative, but not necessarily traditonal camp, are going to say go.
Personally, I would say don’t go. We have been in this position before with an alternating priest who gave heretical sermons. When he would give the sermons, we would have to pull our daughter out of Mass during the sermons. We made a point to not attend Mass at this parish when we knew it was his week to give the sermons, but occassionally he would be there unexpectedly. It became easier not to attend Mass there at all. However, we did not stay home from Mass altogether. We did find another place to attend.
I am not sure where you are located, but surely there must be another place to attend Mass, even if you have to drive a little. Have you checked to see what options you have 30-60 minutes from your home? Perhaps there is a Latin Mass nearer than you think.
Try these 2 links:
web2.airmail.net/carlsch/MaterDei/churches.htm
traditio.com/tradlib/masslat.pdf
The abuses and the general atmosphere of the parish you attend are very important issues. Not only can your faith be weakend by attending there, but that of your children can also be. Some may say that it is the Eucharist you are receiving so it does not matter, but it does. So what if you receive the Eucharist but have lost the faith. How will that help you? Many people receive on Sunday who do not have the faith. That is not profitable to them, it is actually harmful if they are receiving unworthily.
The next thing to consider is the possibility that the Consecration may not be vaild. If the priest is changing the words of the prayers, etc. during Mass, he may also be changing the words of the Consecration. You need to pay attention to know if he is doing this.
You also need to find out if he is using valid matter for the bread and wine. With all of the other abuses, and the relaxed/irreverent atmostphere your described, this may be a possibility. It would not be the first time. Fr. Z recently received an email from someone asking him what to do about a priest using grape juice for the wine. The grape juice is not valid matter and even with the correct words of Consecration does not become the Blood of Christ. Some years ago I remember hearing that it was found that the entire diocese of Cincinnatti had used invalid matter for the hosts for many years. Meaning, the Eucharist was not vaildly consecrated for all of those years. I am not saying this is the case at your parish, however I would look into to it because of all of the toehr abuses you have already mentioned.
Anyway, point is - it is not always a given in that you are receiving the Eucharist. It can be possible that you are not.